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Probabilistic approach to analysis and geometry on metric measure spaces

Research Project

Project/Area Number 22340036
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKumamoto University

Principal Investigator

KUWAE Kazuhiro  熊本大学, 自然科学研究科, 教授 (80243814)

Co-Investigator(Kenkyū-buntansha) SHIOYA Takashi  東北大学, 理学研究科, 教授 (90235507)
OHTA Shinichi  京都大学, 理学研究科, 准教授 (00372558)
KUWADA Kazumasa  東京工業大学, 理学部, 准教授 (30432032)
ISHIWATA Satoshi  山形大学, 理学部, 准教授 (70375393)
Co-Investigator(Renkei-kenkyūsha) ATSUJI Atsushi  慶応大学, 経済学部, 教授 (00221044)
KAWABI Hiroshi  岡山大学, 自然科学研究科, 准教授 (80432904)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2010: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywordsディリクレ形式 / 調和写像 / 劣調和関数 / 変分収束 / グロモフ・ハウスドルフ収束 / アレキサンドロフ空間 / 加藤クラス / 熱核
Research Abstract

We obtained a Jensen's inequality over complete p-uniformly convex spaces. Further we proved the unique existence of the (non-linear) resolvent associated to a coercive proper lower semi continuous function satisfying a weaker notion of p-uniform convexity on a complete metric space and establish the existence of the minimizer of such functions as the large time limit of the non-linear resolvents, which generalizes the pioneering work by J. Jost for harmonic maps into CAT(0)-spaces. The results can be also applied to Lp-Wasserstein space over complete separable p-uniformly convex spaces. As an application, we solve an initial boundary value problem for p-harmonic maps into CAT(0)-spaces in terms of Cheeger type p-Sobolev spaces. On the other hand, we investigated the spectral bounds for symmetric Markov chains with positive n-step coarse Ricci curvature for not only functions but also maps into complete separable 2-uniformly convex spaces with geometric conditions.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (194 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (73 results) (of which Peer Reviewed: 72 results) Presentation (119 results) (of which Invited: 45 results) Remarks (2 results)

  • [Journal Article] Jensen's inequality on convex spaces2014

    • Author(s)
      K. Kuwae
    • Journal Title

      Calc. Var. Partial Differential Equations

      Volume: 49, no.3-4 Pages: 1359-1378

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On spectral bounds for symmetric Markov chains with positive coarse Ricci curvatures2014

    • Author(s)
      E. Kokubo and K. Kuwae
    • Journal Title

      Rev. Romaine Math. Pures Appl

      Volume: 52, no.1 Pages: 123-155

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Examples of spaces with branching geodesics satisfying the curvature-dimension condition2014

    • Author(s)
      S. Ohta
    • Journal Title

      Bull. Lond. Math. Soc

      Volume: 46, no.1 Pages: 19-25

    • NAID

      120005373086

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bochner -Weitzenböck formula and Li-Yau estimates on Finsler manifolds2014

    • Author(s)
      S. Ohta and K.-Th.Sturm
    • Journal Title

      Adv. Math

      Volume: 252 Pages: 429-448

    • NAID

      120005353509

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Jensen's inequality on convex spaces2014

    • Author(s)
      Kazuhiro Kuwae
    • Journal Title

      Calc. Var. Partial Differential Equations

      Volume: 49 Issue: 3-4 Pages: 1359-1378

    • DOI

      10.1007/s00526-013-0625-5

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On spectral bounds for symmetric Markov chains with positive coarse Ricci curvatures2014

    • Author(s)
      Eiki Kokubo and Kazuhiro Kuwae
    • Journal Title

      Rev. Roumaine Math. Pures Appl.

      Volume: 52 Pages: 123-155

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic calculus over symmetric Markov processes with time reversal, preprint2014

    • Author(s)
      Kazuhiro Kuwae
    • Journal Title

      Nagoya Math. J.

      Volume: in press

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms2014

    • Author(s)
      Kazuhiro Kuwae and Yuichi Shiozawa
    • Journal Title

      Math. Nachr.

      Volume: in press

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a stability of heat kernel estimates under generalized non-local Feynman-Kac perturbations for stable-like processes2014

    • Author(s)
      Daehong Kim and Kazuhiro Kuwae
    • Journal Title

      Festschirift on Professor Masatoshi Fukushima

      Volume: in press

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bochner-Weitzenboeck formula and Li-Yau estimates on Finsler manifolds2014

    • Author(s)
      Shin-ichi Ohta and Karl-Theodor Sturm
    • Journal Title

      Adv. Math.

      Volume: 252 Pages: 429-448

    • DOI

      10.1016/j.aim.2013.10.018

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Examples of spaces with branching geodesics satisfying the curvature-dimension condition2014

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      Bull. Lond. Math. Soc.

      Volume: 43 Issue: 1 Pages: 19-25

    • DOI

      10.1112/blms/bdt073

    • NAID

      120005373086

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Splitting theorems for Finsler manifolds of nonnegative Ricci curvature2014

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      J. Reine Angew. Math.

      Volume: in press

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the curvature and heat flow on Hamiltonian systems2014

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      Anal. Geom. Metr. Spaces

      Volume: in press

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A probabilistic approach to the maximal diameter theorem2013

    • Author(s)
      K. Kuwada
    • Journal Title

      Math. Nachr

      Volume: 286, no.4 Pages: 374-378

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gradient estimate for heat kernels, Wasserstein control and Hopf-Lax formula, Potential Theory and its Related Fields2013

    • Author(s)
      K. Kuwada
    • Journal Title

      RIMS Kokyuroku Bessatu

      Volume: B43 Pages: 61-80

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Concentration, Ricci curvature, and eigenvalues of Laplacian2013

    • Author(s)
      K. Funano and T. Shioya
    • Journal Title

      Geom. Func. Anal

      Volume: 23, no.3 Pages: 888-936

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Monotonicity of time-dependent transportation costs and coupling by reflection2013

    • Author(s)
      K. Kuwada and K.-Th.Sturm
    • Journal Title

      Potential Anal

      Volume: 39, no.3 Pages: 231-263

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Caffarelli -Kohn-Nirenberg inequality on metric measure spaces with applications2013

    • Author(s)
      A. Kristaly and S. Ohta
    • Journal Title

      Math. Ann

      Volume: 357, no.2 Pages: 711-726

    • NAID

      120005527983

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Ricci curvature estimates for Hilbert and Funk geometries2013

    • Author(s)
      S. Ohta
    • Journal Title

      Pacific J. Math

      Volume: 265, no.1 Pages: 185-197

    • NAID

      120005399100

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Displacement convexity of generalized relative entropies II2013

    • Author(s)
      S. Ohta and A. Takatsu
    • Journal Title

      Comm. Anal. Geom

      Volume: 21, no.4 Pages: 687-785

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Heat flow on Alexandrov spaces2013

    • Author(s)
      N. Gigli, K. Kuwada and S. Ohta
    • Journal Title

      Comm. Pure Appl. Math

      Volume: 66, no.3 Pages: 307-331

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Concentration, Ricci curvature, and eigenvalues of Laplacian2013

    • Author(s)
      Kei Funano and Takashi Shioya
    • Journal Title

      Geom. Funct. Anal.

      Volume: 23 Issue: 3 Pages: 888-936

    • DOI

      10.1007/s00039-013-0215-x

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Displacement convexity of generalized relative entropies. II2013

    • Author(s)
      Shin-Ichi Ohta and Asuka Takatsu
    • Journal Title

      Comm. Anal. Geom.

      Volume: 21 Issue: 4 Pages: 687-785

    • DOI

      10.4310/cag.2013.v21.n4.a1

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Ricci curvature estimates for Hilbert and Funk geometries2013

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      Pacific J. Math.

      Volume: 265 Issue: 1 Pages: 185-197

    • DOI

      10.2140/pjm.2013.265.185

    • NAID

      120005399100

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications2013

    • Author(s)
      Alexandru Kristaly and Shin-ichi Ohta
    • Journal Title

      Math. Ann.

      Volume: 357 Issue: 2 Pages: 711-726

    • DOI

      10.1007/s00208-013-0918-1

    • NAID

      120005527983

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A probabilistic approach to the maximal diameter theorem.2013

    • Author(s)
      Kazumasa Kuwada
    • Journal Title

      Math. Nachr.

      Volume: 286 Issue: 4 Pages: 374-378

    • DOI

      10.1002/mana.201100330

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Monotonicity of time-dependent transportation costs and coupling by reflection2013

    • Author(s)
      Kazumasa Kuwada and Karl-Theodor Sturm
    • Journal Title

      Potential Anal.

      Volume: 39 Issue: 3 Pages: 231-263

    • DOI

      10.1007/s11118-012-9327-4

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula2013

    • Author(s)
      Kazumasa Kuwada
    • Journal Title

      Potential Theory and its Related Fields, RIMS Kokyuroku Bessatsu

      Volume: B43 Pages: 61-80

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Heat flow on Alexandrov spaces2013

    • Author(s)
      N. Gigli, K. Kuwada and S. Ohta (K. Kuwada)
    • Journal Title

      Comm. Pure Appl. Math.

      Volume: 66 Issue: 3 Pages: 307-331

    • DOI

      10.1002/cpa.21431

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of time -inhomogeneous geodesic random walks and its application to coupling methods2012

    • Author(s)
      K. Kuwada
    • Journal Title

      Ann. Probab

      Volume: 40, no.5 Pages: 1945-1979

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The work of Shin-ichi Ohta2012

    • Author(s)
      T. Shioya
    • Journal Title

      (Japanese) Sugaku

      Volume: 64, no.4 Pages: 408-415

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Barycenters in Alexandrov spaces of curvature bounded below2012

    • Author(s)
      S. Ohta
    • Journal Title

      Adv. Geom

      Volume: 12, no.4 Pages: 571-587

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Calabi's strong maximum principle via local semi-Dirichlet forms2012

    • Author(s)
      K. Kuwae
    • Journal Title

      Potential Anal

      Volume: 37, no.4 Pages: 387-413

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] First variation formula in Wasserstein spaces over compact Alexandrov spaces2012

    • Author(s)
      N. Gigli and S. Ohta
    • Journal Title

      Canad. Math. Bull

      Volume: 55, no.4 Pages: 723-735

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Geometric analysis on Finsler manifolds2012

    • Author(s)
      S. Ohta
    • Journal Title

      (Japanese) Sugaku

      Volume: 64, no.4 Pages: 337-356

    • NAID

      10031177299

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non -contraction of heat flow on Minkowski spaces2012

    • Author(s)
      S. Ohta and K.-Th. Sturm
    • Journal Title

      Arch. Ration. Mech. Anal

      Volume: 204, no.3 Pages: 917-944

    • NAID

      120004161069

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Heat kernel estimates on a connected sum of two copies of R^n along a surface of revolution2012

    • Author(s)
      A. Grigoryan and S. Ishiwata
    • Journal Title

      Global and Stochastic Analysis

      Volume: 2, no.1 Pages: 29-65

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Errata for Stochastic calculus for symmetric Markov processes2012

    • Author(s)
      Z.Q. Chen, P.J. Fitzsimmons, K. Kuwae, T.S. Zhang (K. Kuwae)
    • Journal Title

      Annals of Probability

      Volume: 40 Pages: 1375-1376

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Calabi's strong maximum principle via local semi-Dirichlet forms2012

    • Author(s)
      桑江一洋
    • Journal Title

      Potential Anal

      Volume: 37 Issue: 4 Pages: 387-413

    • DOI

      10.1007/s11118-011-9266-5

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On subharmonicity for symmetric Markov processes2012

    • Author(s)
      Z.-Q. Chen, 桑江一洋
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 64 Issue: 4 Pages: 1181-1209

    • DOI

      10.2969/jmsj/06441181

    • NAID

      10031177265

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Errata Stochastic calculus over symmetric Markov processes without time reversal2012

    • Author(s)
      K. Kuwae
    • Journal Title

      Annals of Probability

      Volume: 40 Issue: 4 Pages: 2705-2706

    • DOI

      10.1214/09-aop516

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The work of Shin-ichi Ohta. (Japanese)2012

    • Author(s)
      T. Shioya
    • Journal Title

      Sugaku

      Volume: 64 Pages: 408-415

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-contraction of heat flow on Minkowski spaces2012

    • Author(s)
      S. Ohta and K. Th. Sturm (S. Ohta)
    • Journal Title

      Arch. Ration. Mech. Anal.

      Volume: 204 Issue: 3 Pages: 917-944

    • DOI

      10.1007/s00205-012-0493-8

    • NAID

      120004161069

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric analysis on Finsler manifolds (Japanese)2012

    • Author(s)
      S. Ohta
    • Journal Title

      Sugaku

      Volume: 64 Pages: 337-356

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] First variation formula in Wasserstein spaces over compact Alexandrov spaces2012

    • Author(s)
      N. Gigli and S. Ohta (S. Ohta)
    • Journal Title

      Canad. Math. Bull.

      Volume: 55 Issue: 4 Pages: 723-735

    • DOI

      10.4153/cmb-2011-110-3

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-explosion of diffusion processes on manifolds with time-dependent metric2012

    • Author(s)
      K. Kuwada and R. Philipowski (K. Kuwada)
    • Journal Title

      Math. Z.

      Volume: 268 Issue: 3-4 Pages: 979-991

    • DOI

      10.1007/s00209-010-0704-7

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods2012

    • Author(s)
      K. Kuwada
    • Journal Title

      Annals of Probability

      Volume: 40 Pages: 1945-1979

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Heat kernel estimates on a connected sum of two copies of Rn along a surface of revolution2012

    • Author(s)
      A. Grigor'yan and S. Ishiwata (S. Ishiwata)
    • Journal Title

      Global and Stochastic Analysis

      Volume: 2 Pages: 29-65

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric analysis of Alexandrov spaces, Su Buqing memorial lectures2011

    • Author(s)
      T. Shioya
    • Journal Title

      Tohoku Math. Publ. Tohoku Univ., Sendai

      Volume: 35, No.1 Pages: 31-46

    • Related Report
      2013 Final Research Report
  • [Journal Article] Collapsing three-manifolds with a lower curvature bound2011

    • Author(s)
      T. Shioya
    • Journal Title

      Tohoku Math. J

      Volume: (2) 63, no.4 Pages: 471-487

    • NAID

      110008764857

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-explosion of diffusion processes on manifolds with time-dependent metric2011

    • Author(s)
      K. Kuwada and R. Philipowski
    • Journal Title

      Math. Z

      Volume: 268, no.3-4 Pages: 979-991

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Coupling of Brownian motions and Perelman's L-functional2011

    • Author(s)
      K. Kuwada and R. Philipowski
    • Journal Title

      J. Funct. Anal

      Volume: 260, no.9 Pages: 2742-2766

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Displacement convexity of generalized relative entropies2011

    • Author(s)
      S. Ohta and A. Takatsu
    • Journal Title

      Adv. Math.

      Volume: 228, no.3 Pages: 1742-1787

    • NAID

      120003405527

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Vanishing S-curvature of Randers spaces2011

    • Author(s)
      S. Ohta
    • Journal Title

      Differential Geom. Appl

      Volume: 29, no.2 Pages: 174-178

    • NAID

      120002970862

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Geometric analysis on Alexandrov spaces [translation of MR2560142]2011

    • Author(s)
      T. Shioya
    • Journal Title

      Sugaku Expositions

      Volume: 24, no.2 Pages: 145-167

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Geometry of probability measure spaces2011

    • Author(s)
      S. Ohta
    • Journal Title

      (Japanese) Sugaku

      Volume: 63, no.1 Pages: 21-42

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A topological splitting theorem for weighted Alexandrov spaces2011

    • Author(s)
      K. Kuwae and T. Shioya
    • Journal Title

      Tohoku Math. J

      Volume: (2)63, no.1 Pages: 59-76

    • NAID

      110008425969

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A TOPOLOGICAL SPLITTING THEOREM FOR WEIGHTED ALEXANDROV SPACES2011

    • Author(s)
      Kazuhiro Kuwae, Takashi Shioya
    • Journal Title

      Tohoku Mathematical Journal, Second Series

      Volume: 63 Issue: 1 Pages: 59-76

    • DOI

      10.2748/tmj/1303219936

    • NAID

      110008425969

    • ISSN
      0040-8735, 2186-585X
    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Invariant sets and ergodic decomposition of local semi-Dirichlet forms2011

    • Author(s)
      桑江一洋
    • Journal Title

      Forum Math

      Volume: 23 Issue: 6 Pages: 1259-1279

    • DOI

      10.1515/form.2011.046

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric Analysis on Alexandrov spaces2011

    • Author(s)
      T.Shioya
    • Journal Title

      Sugaku Expositions

      Volume: 24 Pages: 145-167

    • NAID

      130004558881

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Displacement convexity of generalized relative entropies2011

    • Author(s)
      Shin-ichi Ohta and Asuka Takatsu
    • Journal Title

      Adv. Math

      Volume: 228 Issue: 3 Pages: 1742-1787

    • DOI

      10.1016/j.aim.2011.06.029

    • NAID

      120003405527

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Vanishing S-curvature of Randers spaces2011

    • Author(s)
      S.Ohta
    • Journal Title

      Differentil Geom.Appli.

      Volume: 29 Issue: 2 Pages: 174-178

    • DOI

      10.1016/j.difgeo.2010.12.007

    • NAID

      120002970862

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometry of probability measure spaces2011

    • Author(s)
      S.Ohta
    • Journal Title

      Sugaku

      Volume: 63 Pages: 21-42

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-explosion of diffusion processes on manifolds with time dependent metric2011

    • Author(s)
      K.Kuwada, R.Philipowski
    • Journal Title

      Math.Z.

      Volume: 268 Pages: 979-991

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Coupling Brownian motions and Perelman's L-functional2011

    • Author(s)
      K.Kuwada, R.Philipowski
    • Journal Title

      J.Funct.Anal.

      Volume: 260 Issue: 9 Pages: 2742-2766

    • DOI

      10.1016/j.jfa.2011.01.017

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large deviation for stochastic line integrals as Lp-currents2010

    • Author(s)
      S. Kusuoka, K. Kuwada and Y. Tamura
    • Journal Title

      Probab. Theory Related Fields

      Volume: 147, no.3-4 Pages: 649-674

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Couplings of the Brownian motion via discrete approximation under lower Ricci curvature bounds. Probabilistic approach to geometry2010

    • Author(s)
      K. Kuwada
    • Journal Title

      Adv. Stud. Pure Math, Math. Soc. Japan, Tokyo

      Volume: 57 Pages: 273-292

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infinitesimal Bishop-Gromov condition for Alexandrov spaces, Probabilistic approach to geometry2010

    • Author(s)
      K.Kuwae and T. Shioya
    • Journal Title

      Adv. Stud. Pure Math., Math. Soc. Japan

      Volume: 57 Pages: 293-302

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal transport and Ricci curvature in Finsler geometry. Probabilistic approach to geometry2010

    • Author(s)
      S. Ohta
    • Journal Title

      Adv. Stud. Pure Math, Math. Soc. Japan, Tokyo

      Volume: 57 Pages: 323-342

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Duality on gradient estimates and Wasserstein controls2010

    • Author(s)
      K. Kuwada
    • Journal Title

      J. Funct. Anal

      Volume: 258, no.11 Pages: 3758-3774

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infinitesimal Bishop-Gromov condition for Alexandrov spaces.2010

    • Author(s)
      K.Kuwae, T.Shioya
    • Journal Title

      Adv.Stud.Pure Math

      Volume: 57 Pages: 293-302

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lp-independence of spectral bounds of Feynman-Kac semigroups by continuous additive functionals2010

    • Author(s)
      G.DeLeva, D.Kim, K.Kuwae
    • Journal Title

      J.Funct.Anal.

      Volume: 259 Pages: 690-730

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic calculus over symmetric Markov processes without time reversal2010

    • Author(s)
      K.Kuwae
    • Journal Title

      Ann.Probab.

      Volume: 38 Pages: 1532-1569

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 最適輸送理論と確率解析2014

    • Author(s)
      桑田和正
    • Organizer
      RIMS研究集会「確率解析」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-03-18
    • Related Report
      2013 Final Research Report
  • [Presentation] 空間の集中・収束・消散2014

    • Author(s)
      塩谷隆
    • Organizer
      日本数学会2013年度年会企画特別講演
    • Place of Presentation
      学習院大学
    • Year and Date
      2014-03-17
    • Related Report
      2013 Final Research Report
  • [Presentation] The entropic curvature dimension condition and Bochner's inequality2014

    • Author(s)
      桑田和正
    • Organizer
      Rigidity seminar
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Year and Date
      2014-02-18
    • Related Report
      2013 Final Research Report
  • [Presentation] 空間の集中・収束・消散2014

    • Author(s)
      塩谷隆
    • Organizer
      日本数学会年会 企画特別講演
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The entropic curvature-dimension condition and Bochner’s inequality2014

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      Rigidity seminar
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 最適輸送理論と確率解析2014

    • Author(s)
      桒田 和正
    • Organizer
      確率解析
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The entropic curvature dimension condition and Bochner's inequality2013

    • Author(s)
      桑田和正
    • Organizer
      RIMS 研究集会「確率論シンポジウム」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-12-20
    • Related Report
      2013 Final Research Report
  • [Presentation] The entropic curvature dimension condition and Bochner's inequality2013

    • Author(s)
      桑田和正
    • Organizer
      Conference ProbaGeo 2013 at Luxembourg
    • Place of Presentation
      ルクセンブルグ大学(ルクセンブルグ)
    • Year and Date
      2013-10-31
    • Related Report
      2013 Final Research Report
  • [Presentation] On spectral bounds for symmetric Markov chains with coarse Ricci curvatures2013

    • Author(s)
      桑江一洋
    • Organizer
      Conference ProbaGeo 2013 at Luxembourg
    • Place of Presentation
      ルクセンブルグ大学(ルクセンブルグ)
    • Year and Date
      2013-10-30
    • Related Report
      2013 Final Research Report
  • [Presentation] Global heat kernel upper estimate on connected sums of Riemannian manifolds2013

    • Author(s)
      石渡聡
    • Organizer
      東北大学確率論セミナー
    • Place of Presentation
      東北大学理学研究科数学教室
    • Year and Date
      2013-10-18
    • Related Report
      2013 Final Research Report
  • [Presentation] On spectral bounds for symmetric Markov chains with coarse Ricci curvatures2013

    • Author(s)
      桑江一洋
    • Organizer
      Workshop on geometric aspects in probability and analysis
    • Place of Presentation
      イエナ大学(ドイツ)
    • Year and Date
      2013-09-14
    • Related Report
      2013 Final Research Report
  • [Presentation] Time inhomogeneous couplings of diffusion processes on Riemannian manifolds2013

    • Author(s)
      桑田和正
    • Organizer
      Workshop on geometric aspects in probability and analysis
    • Place of Presentation
      イエナ大学(ドイツ)
    • Year and Date
      2013-09-14
    • Related Report
      2013 Final Research Report
  • [Presentation] The entropic curvature dimension condition and Bochner's inequality2013

    • Author(s)
      桑田和正
    • Organizer
      Dirichlet forms and applications German-Japanese meeting on stochastic analysis
    • Place of Presentation
      ライプチヒ大学(ドイツ)
    • Year and Date
      2013-09-11
    • Related Report
      2013 Final Research Report
  • [Presentation] Resolvent flows for convex functionals and p-harmonic maps2013

    • Author(s)
      桑江一洋
    • Organizer
      Dirichlet forms and applications German-Japanese meeting on stochastic analysis
    • Place of Presentation
      ライプチヒ大学
    • Year and Date
      2013-09-11
    • Related Report
      2013 Final Research Report
  • [Presentation] An extensions of Wasserstein contraction associated with the curvature dimension condition2013

    • Author(s)
      桑田和正
    • Organizer
      The 6th international conference on stochastic analysis and its applications
    • Place of Presentation
      Conference center in Bedlewo, Posnan(ポーランド)
    • Year and Date
      2013-09-10
    • Related Report
      2013 Final Research Report
  • [Presentation] Cheeger type p-Sobolev spaces for CAT(0)-space targets and p-harmonic maps2013

    • Author(s)
      桑江一洋
    • Organizer
      第9回非線形の諸問題
    • Place of Presentation
      高知大学朝倉キャンパス総合研究棟2 階会議室1
    • Year and Date
      2013-09-04
    • Related Report
      2013 Final Research Report
  • [Presentation] The entropic curvature dimension condition and Bochner's inequality2013

    • Author(s)
      桑田和正
    • Organizer
      確率論と幾何学
    • Place of Presentation
      京都大学理学部数学教室大会議室
    • Year and Date
      2013-08-10
    • Related Report
      2013 Final Research Report
  • [Presentation] On the curvature and heat flow on Hamiltonian systems2013

    • Author(s)
      太田慎一
    • Organizer
      確率論と幾何学
    • Place of Presentation
      京都大学理学部数学教室大会議室
    • Year and Date
      2013-08-09
    • Related Report
      2013 Final Research Report
  • [Presentation] p-一様凸空間の勾配流について2013

    • Author(s)
      桑江一洋
    • Organizer
      九州幾何学セミナー
    • Place of Presentation
      九州大学数理学研究院
    • Year and Date
      2013-07-21
    • Related Report
      2013 Final Research Report
  • [Presentation] 凸汎関数の勾配流の構成について2013

    • Author(s)
      桑江一洋
    • Organizer
      東北大学幾何学セミナー
    • Place of Presentation
      東北大学理学研究科数学教室
    • Year and Date
      2013-05-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Concentration, Ricci curvature and eigenvalues of Laplacian, Heat kernels2013

    • Author(s)
      塩谷隆
    • Organizer
      stochastic processes and functional inequalities
    • Place of Presentation
      Oberwalfach 数学研究所(ドイツ)
    • Year and Date
      2013-05-07
    • Related Report
      2013 Final Research Report
  • [Presentation] 結晶格子上の非対称ランダムウォークの漸近挙動,または連結和上の熱核評価2013

    • Author(s)
      石渡聡
    • Organizer
      スペクトル幾何学とその周辺
    • Place of Presentation
      東北大学WPI-AIMR
    • Year and Date
      2013-04-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Extensions of the duality in gradient estimates in Wasserstein controls, Connections for Women on the concentration of measure phenomenon : examples2013

    • Author(s)
      桑田和正
    • Organizer
      applications and links to functional inequalities and to optimal transport
    • Place of Presentation
      名古屋大学
    • Year and Date
      2013-03-14
    • Related Report
      2013 Final Research Report
  • [Presentation] Metric measure geometry of high dimensional spaces2013

    • Author(s)
      塩谷隆
    • Organizer
      The 5th GCOE international symposium on "Weaving Wcience Web beyond Particle-Matter Hierarchy
    • Place of Presentation
      東北大学
    • Year and Date
      2013-03-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Metric measure geometry of high dimensional spaces2013

    • Author(s)
      塩谷隆
    • Organizer
      リーマン幾何と幾何解析
    • Place of Presentation
      筑波大学数学系
    • Year and Date
      2013-02-23
    • Related Report
      2013 Final Research Report
  • [Presentation] Wasserstein contractions associated with the curvature dimension conditions2013

    • Author(s)
      桑田和正
    • Organizer
      マルコフ過程と確率解析
    • Place of Presentation
      京都大学
    • Year and Date
      2013-01-13
    • Related Report
      2013 Final Research Report
  • [Presentation] 凸汎関数の勾配流の構成について2013

    • Author(s)
      桑江一洋
    • Organizer
      東北大学幾何学セミナー
    • Place of Presentation
      東北大学大学院理学研究科数学専攻
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] p-一様凸空間上の凸汎関数の勾配流について2013

    • Author(s)
      桑江一洋
    • Organizer
      九州大学幾何学セミナー
    • Place of Presentation
      九州大学大学院数理学研究院
    • Related Report
      2013 Annual Research Report
  • [Presentation] Cheeger type p-Sobolev spaces for CAT(0)-space targets and p-harmonic maps2013

    • Author(s)
      桑江一洋
    • Organizer
      第9回非線形の諸問題
    • Place of Presentation
      高知大学朝倉キャンパス 総合研究棟2階 会議室1
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Resolvent ows for convex functionals and p-harmonic maps2013

    • Author(s)
      Kazuhiro Kuwae
    • Organizer
      Dirichlet Forms and Applications German-Japanese Meeting on Stochastic Analysis
    • Place of Presentation
      Mathematisches Institut der Universitaet Leipzig
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On spectral bounds for symmetric Markov chains with coarse Ricci curvatures2013

    • Author(s)
      Kazuhiro Kuwae
    • Organizer
      Workshop on Geometric aspects in probability and analysis
    • Place of Presentation
      Ernst Abbe Platz 2, fifth floor, Room 3517, Friedrich Schiller University Jena
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On spectral bounds for symmetric Markov chains with coarse Ricci curvatures2013

    • Author(s)
      Kazuhiro Kuwae
    • Organizer
      Conference ProbaGeo 2013 at Luxembourg
    • Place of Presentation
      University of Luxembourg
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Another analytic characterization of gaugeability for generalized Feynman-Kac functionals2013

    • Author(s)
      桑江一洋
    • Organizer
      マルコフ過程とその周辺
    • Place of Presentation
      東北大学理学部数学科川井ホール
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On a stability for generalized Feynman-Kac semigroups of stable-like processes2013

    • Author(s)
      桑江 一洋
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Concentration, Ricci curvature, and eigenvalues of Laplacian2013

    • Author(s)
      Takashi Shioya
    • Organizer
      Heat Kernels, Stochastic Processes and Functional Inequalities
    • Place of Presentation
      Oberwolfach数学研究所(ドイツ)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the curvature and heat flow on Hamiltonian systems2013

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      Geometry and probability
    • Place of Presentation
      京都大学理学研究科数学教室
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The entropic curvature dimension condition and Bochner’s inequality2013

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      Geometry and probability
    • Place of Presentation
      京都大学理学研究科数学教室
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Entropic curvature dimension condition and Bochner’s inequality2013

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      Dirichlet forms and applications, German-Japanese conference on stochastic analysis
    • Place of Presentation
      University of Leipzig, Germany
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Time inhomogeneous couplings for diffusion processes on Riemannian manifolds2013

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      Geometric aspects in probability and analysis
    • Place of Presentation
      University of Jena, Germany
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The entropic curvature-dimension condition and Bochner’s inequality2013

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      Conference ProbaGeo 2013
    • Place of Presentation
      University of Luxembourg, Luxembourg
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The entropic curvature dimension condition and Bochner’s inequality2013

    • Author(s)
      桒田 和正
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 結晶格子上の非対称ランダム・ウォークの漸近挙動、または連結和上の熱核評価2013

    • Author(s)
      石渡 聡
    • Organizer
      スペクトル幾何学とその周辺
    • Place of Presentation
      東北大学WPI-AIMR
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Global heat kernel upper esitmate on connected sums of Riemannian Manifolds2013

    • Author(s)
      石渡 聡
    • Organizer
      東北確率論セミナー
    • Place of Presentation
      東北大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Large deviation principles for generalized Feynman-Kac functionals and Lp-independence of spectral radius2013

    • Author(s)
      Kazuhiro Kuwae
    • Organizer
      Stochastic Seminar
    • Place of Presentation
      AMSS(Academy of Mathematics and Systems Science) CAS(Chinese Academy of Science), 北京, 中華人民共和国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Metric measure geometry for high-dimensional spaces2013

    • Author(s)
      塩谷隆
    • Organizer
      リーマン幾何と幾何解析
    • Place of Presentation
      筑波大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Metric measure geometry of high-dimensional spaces2013

    • Author(s)
      塩谷隆
    • Organizer
      The 5th GCOE Internal Symposium on "Weaving Science Web beyond Particle-Matter Hierarchy"
    • Place of Presentation
      東北大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Wasserstein contractions associated with the curvature-dimension condition2013

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      マルコフ過程と確率解析
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Extensions of the duality in gradient estimates and Wasserstein controls2013

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      Connections for Women on the concentration of measure phenomenon :examples, applications and links to functional inequalities and to optimal transport
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On spectral bounds for symmetric Markov chains with coarse Ricci curvatures2012

    • Author(s)
      桑江一洋
    • Organizer
      RIMS 研究集会「確率論シンポジウム」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-12-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Heat kernel estimates on a connected sum along a joint with a capacity growth2012

    • Author(s)
      石渡聡
    • Organizer
      Advances in fractals and related topics
    • Place of Presentation
      香港中文大学, 香港(中華人民共和国)
    • Year and Date
      2012-12-11
    • Related Report
      2013 Final Research Report
  • [Presentation] 連結和上の熱核評価2012

    • Author(s)
      石渡聡
    • Organizer
      多様体上の微分方程式
    • Place of Presentation
      金沢大学サテライトプラザ
    • Year and Date
      2012-11-17
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] Wasserstein contractions associated with the curvature dimension conditions2012

    • Author(s)
      桑田和正
    • Organizer
      ERC Workshop on optimal transportaion and applications
    • Place of Presentation
      Scuola Normale Superiore,Pisa(イタリア)
    • Year and Date
      2012-11-09
    • Related Report
      2013 Final Research Report
  • [Presentation] On Ricci curvature for Lagrangean/Hamiltonian systems2012

    • Author(s)
      太田慎一
    • Organizer
      ERC Workshop on optimal transportaion and applications
    • Place of Presentation
      Scuola Normale Superiore,Pisa( イタリア)
    • Year and Date
      2012-11-05
    • Related Report
      2013 Final Research Report
  • [Presentation] On spectral bounds for symmetric Markov chains with coarse Ricci curvatures2012

    • Author(s)
      桑江一洋
    • Organizer
      Dirichlet forms and applications German-Japanese meeting on stochastic analysis
    • Place of Presentation
      岡山大学
    • Year and Date
      2012-09-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Wasserstein contractions associated with the curvature dimension conditions2012

    • Author(s)
      桑田和正
    • Organizer
      Dirichlet forms and applications German-Japanese meeting on stochastic analysis
    • Place of Presentation
      岡山大学
    • Year and Date
      2012-09-27
    • Related Report
      2013 Final Research Report
  • [Presentation] 熱分布の結合法と次元曲率条件2012

    • Author(s)
      桑田和正
    • Organizer
      日本数学会秋期分化会統計数学分化会特別講演
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Ricci curvature in Finsler geometry and applications2012

    • Author(s)
      太田慎一
    • Organizer
      MSJ-KMS joint meeting
    • Place of Presentation
      九州大学医学部百周年記念講堂
    • Year and Date
      2012-09-17
    • Related Report
      2013 Final Research Report
  • [Presentation] Ricci curvature in Finsler geometry and applications2012

    • Author(s)
      太 田慎一
    • Organizer
      The 8th China-Japan friendship conference on differential geometry
    • Place of Presentation
      四川大学, 成都(中華人民共和国)
    • Year and Date
      2012-09-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Applications of Hopf-Lax formulae to analysis of heat distributions2012

    • Author(s)
      桑田和正
    • Organizer
      RIMS 研究集会「Potential theory and related fields」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-09-04
    • Related Report
      2013 Final Research Report
  • [Presentation] Ricci curvature in Finsler geometry and applications2012

    • Author(s)
      太田慎一
    • Organizer
      The 4th geometry meeting dedicated to the centenary of A.D. Alexandrov
    • Place of Presentation
      Euler institute, Saint-Petersburg(ロシア)
    • Year and Date
      2012-08-21
    • Related Report
      2013 Final Research Report
  • [Presentation] On non-linear spectral gap for symmetric Markov processes with coarse Ricci curvatures2012

    • Author(s)
      桑江一洋
    • Organizer
      The 4th geometry meeting dedicated to the centenary of A.D. Alexnadrov
    • Place of Presentation
      Euler institute, Saint -Petersburg(ロシア)
    • Year and Date
      2012-08-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Concentration, Ricci curvature, and eigenvalues of Laplacian2012

    • Author(s)
      塩谷隆
    • Organizer
      The 4th geometry meeting dedicated to the centenary of A.D. Alexnadrov
    • Place of Presentation
      Euler institute, Saint-Petersburg(ロシア)
    • Year and Date
      2012-08-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Optimal transportation costs of heat distribution in stochastic geometry analysis, UK-Japan mathematical forum on geometry, probability and their applications2012

    • Author(s)
      桑田和正
    • Organizer
      BIRS workshop "Optimal transport and differential geometry"
    • Place of Presentation
      慶応大学
    • Year and Date
      2012-07-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Ricci curvature bounds and heat flow on metric measure spaces2012

    • Author(s)
      太 田慎一
    • Organizer
      National center for theoretical sciences
    • Place of Presentation
      台湾国立大学(中華民国)
    • Year and Date
      2012-07-10
    • Related Report
      2013 Final Research Report
  • [Presentation] On non-linear spectral gap for symmetric Markov processes with coarse Ricci curvatures2012

    • Author(s)
      桑江一洋
    • Organizer
      RIMS 研究集会「変分問題の展開-確率論と交錯する変分問題」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-06-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Curvature dimension condition and heat flow on metric measure spaces2012

    • Author(s)
      太田慎一
    • Organizer
      RIMS 研究集会「変分問題の展開-確率論と交錯する変分問題」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-06-10
    • Related Report
      2013 Final Research Report
  • [Presentation] 非コンパクトな連結部分をもつ連結和上の熱核評価2012

    • Author(s)
      石渡聡
    • Organizer
      東北大学幾何学セミナー
    • Place of Presentation
      東北大学理学研究科数学教室
    • Year and Date
      2012-06-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Splitting theorems of Finsler manifolds with non-negative Ricci curvatures2012

    • Author(s)
      太田慎一
    • Organizer
      Conference on geometry
    • Place of Presentation
      京都大学
    • Year and Date
      2012-05-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Monotonicity of time-dependent transportation costs and coupling by reflection2012

    • Author(s)
      桑田和正
    • Organizer
      BIRS workshop "Optimal transport and differential geometry"
    • Place of Presentation
      BIRS, Banff(カナダ)
    • Year and Date
      2012-05-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Splitting theorems of Finsler manifolds with non-negative Ricci curvatures2012

    • Author(s)
      太田慎一
    • Organizer
      BIRS workshop "Optimal transport and differential geometry"
    • Place of Presentation
      BIRS, Banff(カナダ)
    • Year and Date
      2012-05-20
    • Related Report
      2013 Final Research Report
  • [Presentation] 測度距離空間のリッチ曲率と熱流2012

    • Author(s)
      太田慎一
    • Organizer
      日本数学会年会総合講演
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-27
    • Related Report
      2013 Final Research Report
  • [Presentation] 測度距離空間のリッチ曲率と熱流2012

    • Author(s)
      太田慎一
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学(東京)(招待講演)
    • Year and Date
      2012-03-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] Heat kernel estimates on connected sums with non-compact joint2012

    • Author(s)
      石渡聡
    • Organizer
      Weekly Seminar
    • Place of Presentation
      香港中文大学(中華人民共和国)
    • Year and Date
      2012-03-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Heat kernel estimates on connected sums with non-compact joint2012

    • Author(s)
      石渡聡
    • Organizer
      Weekly Seminar
    • Place of Presentation
      香港中文大学(中華人民共和国)(招待講演)
    • Year and Date
      2012-03-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Markov chains with Ollivier's coarse Ricci curvature and harmonic maps into convex spaces2012

    • Author(s)
      桑江一洋
    • Organizer
      第13回非線形偏微分方程式研究会
    • Place of Presentation
      早稲田大学教育学部14号館4階401号室
    • Year and Date
      2012-03-06
    • Related Report
      2013 Final Research Report
  • [Presentation] Markov chains with OUivier's coarse Ricci curvature and harmonic maps into convex spaces2012

    • Author(s)
      K.Kuwae
    • Organizer
      第13回非線形偏微分方程式研究会
    • Place of Presentation
      早稲田大学教育学部14号館4階401号室(東京)(招待講演)
    • Year and Date
      2012-03-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] Heat kernel estimates on connected sums with non-compact joint2012

    • Author(s)
      石渡聡
    • Organizer
      Cornell Analysis Seminar
    • Place of Presentation
      Cornell 大学(米国)
    • Year and Date
      2012-01-23
    • Related Report
      2013 Final Research Report
  • [Presentation] Heat kernel estimates on connected sums with non-compact joint2012

    • Author(s)
      石渡聡
    • Organizer
      Cornell Analysis Seminar
    • Place of Presentation
      Cornell大学(米国)(招待講演)
    • Year and Date
      2012-01-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] Concentration of metric measure spaces2012

    • Author(s)
      塩谷隆
    • Organizer
      geometric measure theory in non-Euclidean spaces
    • Place of Presentation
      Scuola Normale Superiore,Pisa (イタリア)
    • Related Report
      2013 Final Research Report
  • [Presentation] On non-linear spectral gap for symmetric Markov chains with coarse Ricci curvature2012

    • Author(s)
      桑江一洋
    • Organizer
      RIMS 研究集会「変分問題の展開-確率論と交錯する変分問題」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On non-linear spectral gap for symmetric Markov chains with coarse Ricci curvature2012

    • Author(s)
      Kazuhiro Kuwae
    • Organizer
      The Fourth Geometry Meeting dedicated to the centenary of A.D.Alexandrov
    • Place of Presentation
      Euler Institute, Saint-Petersburg, Russia
    • Related Report
      2012 Annual Research Report
  • [Presentation] On analytic characterizations of gaugeability for generalized Feynman-Kac functionals2012

    • Author(s)
      Kazuhiro Kuwae
    • Organizer
      6th International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      Conference Center in Bedlewo, Posnan, Poland
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On spectral bounds for symmetric Markov chains with coarse Ricci curvatures2012

    • Author(s)
      Kazuhiro Kuwae
    • Organizer
      Stochastic analysis and applications (German-Japanese bilateral reserch project)
    • Place of Presentation
      岡山大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Analytic characterizations of gaugeability for generalized Feynman-Kac functionals2012

    • Author(s)
      Kazuhiro Kuwae
    • Organizer
      Workshop on Stochastic Analysis and Related Topics
    • Place of Presentation
      AMSS(Academy of Mathematics and Systems Science) CAS(Chinese Academy of Science), 北京, 中華人民共和国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On spectral bounds for symmetric Markov chains with coarse Ricci curvatures2012

    • Author(s)
      桑江一洋
    • Organizer
      RIMS 研究集会「 確率論シンポジウム」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
  • [Presentation] Concentration of metric measure spaces, Analysis and Geometry in Metric Measure Spaces2012

    • Author(s)
      Takashi Shioya
    • Organizer
      Geometric Measure Theory in non-Euclidean Spaces
    • Place of Presentation
      Scuola Normale Superiore, Pisa, Italy
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] oncentration, Ricci curvature, and eigenvalues of Laplacian2012

    • Author(s)
      Takashi Shioya
    • Organizer
      The Fourth Geometry Meeting dedicated to the centenary of A.D.Alexandrov
    • Place of Presentation
      Euler Institute, Saint-Petersburg, Russia
    • Related Report
      2012 Annual Research Report
  • [Presentation] Monotonicity of time-dependent transportation costs and coupling by reflection2012

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      BIRS workshop "Optimal transportation and differential geometry"
    • Place of Presentation
      BIRS, Banff, Canada
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Optimal transportation costs of heat distributions in stochastic geometric analysis2012

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      UK-Japan mathematical forum on geometry, probability and their applications
    • Place of Presentation
      慶応大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Applications of Hopf-Lax formulae to analysis of heat distributions2012

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      RIMS 研究集会「 Potential theory and its related fields」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] An extension of Wasserstein contraction associated with the curvature-dimension condition2012

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      6th International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      Conference Center in Bedlewo, Posnan, Poland
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 熱分布の結合法と次元曲率条件2012

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      日本数学会 2012年度秋期総合分科会 統計数学分科会 特別講演
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Wasserstein contractions associated with the curvature-dimension condition2012

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      Stochastic analysis and applications (German-Japanese bilateral reserch project)
    • Place of Presentation
      岡山大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Wasserstein contractions associated with the curvature-dimension condition2012

    • Author(s)
      Kazumasa Kuwada
    • Organizer
      ERC Workshop on Optimal Transportation and Applications
    • Place of Presentation
      Scuola Normale Superiore, Pisa, Italy
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Splitting theorems for Finsler manifolds of nonnegative Ricci curvature2012

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      IRS workshop "Optimal transportation and differential geometry"
    • Place of Presentation
      BIRS, Banff, Canada
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Splitting theorems for Finsler manifolds of nonnegative Ricci curvature2012

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      Conference on Geometry
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Curvature-dimension condition and heat flow on metric measure spaces2012

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      RIMS 研究集会「変分問題の展開–確率論と交錯する変分問題」
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Ricci curvature bounds and heat flow on metric measure spaces2012

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      National Center for Theoretical Sciences
    • Place of Presentation
      台湾国立大学, 中華民国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Ricci Curvature in Finsler Geomtery and Applications2012

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      The Fourth Geometry Meeting dedicated to the centenary of A.D.Alexandrov
    • Place of Presentation
      Euler Institute, Saint-Petersburg, Russia
    • Related Report
      2012 Annual Research Report
  • [Presentation] Ricci curvature in Finsler geometry and applications2012

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      The eighth China-Japan Friendship Conference on Differential Geometry
    • Place of Presentation
      Sichuan University, Chengdu, China.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Ricci curvature in Finsler geometry and applications2012

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      MSJ-KMS Joint Meeting
    • Place of Presentation
      九州大学医学部百周年記念講堂
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On Ricci Curvature for Lagrangian/Hamiltonian Systems2012

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      ERC Workshop on Optimal Transportation and Applications
    • Place of Presentation
      Scuola Normale Superiore, Pisa, Italy
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 非コンパクトな連結部分を持つ連結和上の熱核評価2012

    • Author(s)
      石渡聡
    • Organizer
      東北大学幾何学セミナー
    • Place of Presentation
      東北大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Heat kernel estimates on a connected sum along a joing with a capacity growth2012

    • Author(s)
      石渡聡
    • Organizer
      Advances on Fractals and Related Topics
    • Place of Presentation
      香港中文大学 中華人民共和国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Wasserstein 距離にまつわる確率解析I2011

    • Author(s)
      桑田和正
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      関西大学千里山キャンパス
    • Year and Date
      2011-12-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Wasserstein 距離にまつわる確率解析II2011

    • Author(s)
      桑田和正
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      関西大学千里山キャンパス
    • Year and Date
      2011-12-20
    • Related Report
      2013 Final Research Report
  • [Presentation] フィンスラー多様体のリッチ曲率2011

    • Author(s)
      太田慎一
    • Organizer
      日本数学会秋期総合分科会幾何学分科会特別講演
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-29
    • Related Report
      2013 Final Research Report
  • [Presentation] フィンスラー多様体のリッチ曲率2011

    • Author(s)
      太田慎一
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      信州大学(長野)(招待講演)
    • Year and Date
      2011-09-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Optimal transport and coupled diffusion by reflection2011

    • Author(s)
      桑田和正
    • Organizer
      5th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      ボン大学(ドイツ)
    • Year and Date
      2011-09-06
    • Related Report
      2013 Final Research Report
  • [Presentation] Concentration, Ricci curvature, and eigenvalues of Laplacian2011

    • Author(s)
      塩谷隆
    • Organizer
      Metric geometry and applications
    • Place of Presentation
      南京(中華人民共和国)
    • Year and Date
      2011-07-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Concentration, Ricci curvature, and eigenvalues of Laplacian metric geometry and applications2011

    • Author(s)
      T.Shioya
    • Organizer
      Metric geometry and applications
    • Place of Presentation
      南京(中華人民共和国)(招待講演)
    • Year and Date
      2011-07-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Heat flow for Alexandrov spaces2011

    • Author(s)
      桑田和正
    • Organizer
      The 35th SPA
    • Place of Presentation
      Oaxaca(メキシコ)
    • Year and Date
      2011-06-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Heat flow for Alexandrov spaces2011

    • Author(s)
      K.Kuwada
    • Organizer
      The 35^<th> SPA
    • Place of Presentation
      Oaxaca (Mexico)(招待講演)
    • Year and Date
      2011-06-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] Jensen's inequality on convex spaces2011

    • Author(s)
      桑江一洋
    • Organizer
      日本数学会年会一般講演
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Displacement convexity of generalized relative entropies2010

    • Author(s)
      太 田慎一
    • Organizer
      The 34th SPA
    • Place of Presentation
      千里ライフサイエンスセンター(大阪)
    • Year and Date
      2010-09-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Geometric and probabilistic aspects of p-uniformly convex spaces2010

    • Author(s)
      桑江一洋
    • Organizer
      The 6th Geometry Conference for Friendship of China and Japan
    • Place of Presentation
      西北大学非線形科学研究センター, 西安(中華人民共和国)
    • Year and Date
      2010-09-04
    • Related Report
      2013 Final Research Report
  • [Presentation] On non-linear martingales taking values into convex spaces2010

    • Author(s)
      桑江一洋
    • Organizer
      The 4th International Conference on Stochastic Analysis and Its Application
    • Place of Presentation
      関西大学千里山キャンパス
    • Year and Date
      2010-08-31
    • Related Report
      2013 Final Research Report
  • [Presentation] On non-linear martingales taking values into convex spaces2010

    • Author(s)
      K.Kuwae
    • Organizer
      The 4th International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      関西大学千里山キャンパス
    • Year and Date
      2010-08-31
    • Related Report
      2010 Annual Research Report
  • [Presentation] Variational convergence over convex spaces2010

    • Author(s)
      桑江一洋
    • Organizer
      確率論と幾何学
    • Place of Presentation
      東北大学
    • Year and Date
      2010-08-26
    • Related Report
      2013 Final Research Report
  • [Remarks] 集中講義①「確率測度の空間上の解析学と幾何学(最適輸送理論とマルコフ連鎖)」名古屋大学多元数理科学研究科(2012年1月)

    • Related Report
      2013 Final Research Report
  • [Remarks] 熊本大学自然科学研究科による研究内容紹介

    • URL

      http://www.gsst.kumamoto-u.ac.jp/kenkyu/pdf/jyouho/ouyou/kuwae.pdf

    • Related Report
      2013 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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