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Study of convergence and collapsing phenomena by methods of geometric analysis

Research Project

Project/Area Number 21340013
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionUniversity of Tsukuba

Principal Investigator

YAMAGUCHI Takao  筑波大学, 数理物質系, 教授 (00182444)

Co-Investigator(Kenkyū-buntansha) SHIOYA Takashi  東北大学, 大学院・理学研究科, 教授 (90235507)
ISOZAKI Hiroshi  筑波大学, 数理物質系, 教授 (90111913)
NAGANO Koichi  筑波大学, 数理物質系, 講師 (30333777)
Project Period (FY) 2009-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥17,030,000 (Direct Cost: ¥13,100,000、Indirect Cost: ¥3,930,000)
Fiscal Year 2013: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2011: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2010: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2009: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Keywords崩壊理論 / グロモフ・ハウスドルフ収束 / スペクトル逆問題 / アレクサンドロフ空間 / 幾何解析 / 測度距離空間 / リプシッツ可縮 / 崩壊 / 国際研究者交流 / リッチ流 / プラス・ベルトラミ作用素
Research Abstract

We obtained the uniqueness and the stability of the inverse spectral problem
concerning the local data of the heat kernels in the moduli of closed Rimennian manifolds whose sectional curvature and diameters are uniformly bounded (T.Yamaguchi, S. Kurylev, M.Lassas). We classified the collapsing phenomena of three-dimensional closed Alexandrov spaces with cuvature uniformly bounded below. Moreover we proved the local strong Lipschitz contractibility of Alexandrov spaces and the stability of strongly Lipschitz contractible balls(T.Yamaguchi, A.Mitsuishi). We proved that the curvature dimension condition of Ricci curvature is preserved under the concentration of metric measure spaces(T.Shioya, K.Funano). We reconstructed hyperbolic orbifolds from S-matirix corresponding to a general end (H. Isozaki, Y. Kurylev).

Report

(6 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (73 results)

All 2014 2013 2012 2011 2010 2009 Other

All Journal Article (33 results) (of which Peer Reviewed: 32 results) Presentation (39 results) (of which Invited: 4 results) Book (1 results)

  • [Journal Article] Inverse boundary value problems for the perturbed polyharmonic operator2014

    • Author(s)
      Krupchyk, K; lLassas, Matti; Uhlmann, G.
    • Journal Title

      Trans. AMS.

      Volume: 366 Pages: 95-112

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

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

      Geom. Funct. Anal

      Volume: 23 Pages: 888-936

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse problems for time-dependent singular heat conductivities ; One-dimensional case2013

    • Author(s)
      P. Gaitan, H. Isozaki, O. Poisson, S. Siltanen and J. Tamminenn
    • Journal Title

      SIAM J. Math. Anal

      Volume: NO 3 Pages: 1675-1690

    • NAID

      120007136874

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

    • Author(s)
      Funano, Kei; Shioya Takashi
    • Journal Title

      Geom. Funct. Anal.

      Volume: 23 Pages: 888-936

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inverse problems for time-dependent singular heat conductivities-one dimensional case2013

    • Author(s)
      Gitan,P.; Isozaki,Hiroshi; Poisson, O.; Siltanen, S; Tamminen, J
    • Journal Title

      SIAM J. Msth. Anal.

      Volume: 45 Pages: 1675-1690

    • NAID

      120007136874

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Proving for heat conductive bodies2012

    • Author(s)
      P. Gaitan, H. Isozaki, O. Poisson, S. Siltan en and J. Tamminenn
    • Journal Title

      Inverse Problems and Imaging

      Volume: 6 Pages: 423-446

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the wave operators for the Friedrichs-Faddeev model2012

    • Author(s)
      H. Isozaki and S. Richard
    • Journal Title

      Ann. Henri Poincare

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse problems, trace formula for discrete Schroedinger operators2012

    • Author(s)
      H. Isozaki and E. Korotyaev
    • Journal Title

      Ann. Henri Poincare

      Volume: 13 Pages: 751-788

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse problems, trace formulae for discrete Schrodenger operators2012

    • Author(s)
      H. isozaki and E. Korotyaev
    • Journal Title

      Ann. Henri Poincare

      Volume: 13 Pages: 751-788

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gemetric Analysis on Alexandrov spaces2011

    • Author(s)
      Shioya, Takashi
    • Journal Title

      Sugaku Exposision 24

      Pages: 145-167

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

    • Author(s)
      Shioya, Takashi
    • Journal Title

      Tohoku math. J.

      Volume: 63 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)
      Kuwae, Kazuhiro; Shiova, Takashi
    • Journal Title

      Tohoku Math.J.

      Volume: 63 Pages: 59-76

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gauge equivalence and inverse scattering for long-range magnetic potentials2011

    • Author(s)
      Eskin, G.; Isozaki, H.
    • Journal Title

      Russ.J.Math.Phys.

      Volume: 18 Pages: 2164-2194

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reconstruction of collapsed manifolds2010

    • Author(s)
      Yamaguchi, Takao
    • Journal Title

      Proceeding of ICM2010

      Volume: VolII Pages: 899-913

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infinitesimal Bishop-Gromov condition for Alexandrov spaces2010

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

      Probabilistic approach to geometry

      Volume: 56 Pages: 293-302

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gauge equivalence and inverse scattering for long-range magnetic potentials2010

    • Author(s)
      G. Eskin and H. Isozaki
    • Journal Title

      Russian J. of Math. Phys.

      Volume: Vol 18 Pages: 19-28

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gauge equivalence and inverse scattering for Ahoronov-Bohm effect2010

    • Author(s)
      G. Eskin, H. Isozaki and S. O' dell
    • Journal Title

      Commun. in P. D. E.

      Volume: 35 Pages: 1-31

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Forward and inverse scattering problem on manifolds with asymptotically cylindrical ends2010

    • Author(s)
      H. Isozaki, Y. Kurylev and M. Lassas
    • Journal Title

      Journal of Funct. Anal.

      Volume: 258 Pages: 2060-2118

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Local detection of three dimensional inclusions in electrical impedance tomography2010

    • Author(s)
      T. Ide, H. Isozaki, S. Nakata and S. Siltanen
    • Journal Title

      Inverse Problems

      Volume: 26 No. 3

    • NAID

      120007138215

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reconstruction of collapsed manifolds2010

    • Author(s)
      Yamaguchi, Takao
    • Journal Title

      Proceedings of the International Congress of Mathematicians

      Volume: Volume II Pages: 899-913

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reconstructionofcollapsedmanifolds2010

    • Author(s)
      Yamaguchi, Takao
    • Journal Title

      Proceedings of ICM 2010

      Volume: (To appear)

    • Related Report
      2010 Annual Research Report
  • [Journal Article] InfinitesimalBishop.GromovconditionforAlexandrovspaces,Prpbabilistisapproachtogeometry2010

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

      Adv.Stud.Pure Math.

      Volume: 57 Pages: 293-302

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Forwardandinversescatteringonmanifoldswithasymptoticallycylindricalends2010

    • Author(s)
      Isozaki, Hiroshi Kurylev, Yaroslav, Lassas, Matti
    • Journal Title

      J.Funct.Anal.

      Volume: 258 Pages: 2060-2118

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Localdetectionofthree-dimensionalinclusionsinelectricalimpedencetomography2010

    • Author(s)
      Ide, T., Isozaki, H., Nakata, S., Siltanen,S.
    • Journal Title

      Inverse Problems

      Volume: 26 Pages: 1-17

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An upper curvature bound and singularities2009

    • Author(s)
      Yamaguchi, Takao
    • Journal Title

      Non commutativity and Singularities, Advanced Studies in Pure Mathematics

      Volume: 55 Pages: 161-171

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pseudodifferential multiproduct representation of the solution operator of a parabolic equation2009

    • Author(s)
      H. Isozaki and J. Rousseau
    • Journal Title

      Comm. in P. D. E.

      Volume: 34 Pages: 625-655

    • NAID

      120007137999

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] An upper curvature bound and singularities2009

    • Author(s)
      Yamaguchi, Takao
    • Journal Title

      Noncommutativity and Singularities, Advanced Studies in Pure Mathematics 55

      Pages: 161-171

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric analysis on Alexandrov spaces(Japanese)2009

    • Author(s)
      Shioya, Takashi
    • Journal Title

      Sugaku 61

      Pages: 1-20

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pseudodifferential multi-product representation of the solution operator of aparabolic equation2009

    • Author(s)
      Isozaki, Hiroshi ; Le Rousseau, Jerome
    • Journal Title

      Comm.Partial Differential Equations 34

      Pages: 625-655

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of strongly Lipschitz contractible balls in Alexandrov spaces

    • Author(s)
      Mitsuishi Ayato and Yamaguchi, Takao
    • Journal Title

      Math. Zeit

      Volume: (印刷中)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Locally Lipschitz contractibility of Alexandrov spaces

    • Author(s)
      Mitsuishi Ayato and Yamaguchi, Takao
    • Journal Title

      Pacific J Math

      Volume: (印刷中)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Collapsing three-dimensional Alexandrov spaces with a lower curvature bound

    • Author(s)
      Mitsuishi Ayato and Yamaguchi, Takao
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: (印刷中)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Rellich type theorem for discrete Schroedinger operators

    • Author(s)
      H. Isozaki and H. Morioka
    • Journal Title

      Inverse Problems and Imaging

      Volume: (印刷中)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Presentation] Collapsing three dimensional Alexandrov spaces I, II2013

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      Moduli spaces of low dimensional manifolds
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-11-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse spectral theory and the Minkowski problem for the surface of revolution2013

    • Author(s)
      磯崎洋
    • Organizer
      広島微分方程式研究会
    • Place of Presentation
      広島大学
    • Year and Date
      2013-10-11
    • Related Report
      2013 Final Research Report
  • [Presentation] オービフォールド・カスプ・逆散乱2013

    • Author(s)
      磯崎洋
    • Organizer
      実函数論・ 函数解析合同シンポジウ ム
    • Place of Presentation
      青山学院大学
    • Year and Date
      2013-09-05
    • Related Report
      2013 Final Research Report
  • [Presentation] 崩壊とスペクトル逆問題2013

    • Author(s)
      山口 孝男
    • Organizer
      第60回幾何学シンポジウム基調講演
    • Place of Presentation
      東京工業大学
    • Year and Date
      2013-08-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Collapsing manifolds and inverse spectral problems2013

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      Collapsing manifolds and inverse spectral problems
    • Place of Presentation
      Kyoto University
    • Year and Date
      2013-08-10
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse problems for time-dependent heat conductivities in multi-dimensions2013

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      AppliedInverse Problems Conference at KAIST
    • Place of Presentation
      Daejeon, Korea
    • Year and Date
      2013-07-03
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse scattering on asymptotically hyperbolic orbifolds2013

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      SpectralTheory and Partial Differential Equations (UCLA)
    • Place of Presentation
      USA
    • Year and Date
      2013-06-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse scattering on perturbed lattice2013

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      Workshop "Inverse Problems and Applications"
    • Place of Presentation
      Mittag-Leffler Institute
    • Year and Date
      2013-04-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Metric measure geometry of high-dimensional spaces2013

    • Author(s)
      Shioya, Takashi
    • Organizer
      The 5th GCOE Internal Symposium on "Weaving Science 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 for high-dimensional spaces2013

    • Author(s)
      塩谷 隆
    • Organizer
      研究会「リーマン幾何と幾何解析」
    • Place of Presentation
      筑波大学
    • Year and Date
      2013-02-23
    • Related Report
      2013 Final Research Report
  • [Presentation] Spec tral theory and inverse problems for discrete Schroedinger operators2012

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      Taiwan-Japan joint conference on PDE and analysis
    • Place of Presentation
      台湾大学
    • Year and Date
      2012-12-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse scattering for discrete Schroedinger operators2012

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      Seminaire d' EDP
    • Place of Presentation
      フランス
    • Year and Date
      2012-12-06
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse cattering for discrete Schroedinger operators2012

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      Inverse problems and pplications
    • Place of Presentation
      (Hangzhou) , China
    • Year and Date
      2012-09-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Concentration, Ricci curvature, and eigenvalues of Laplacian2012

    • Author(s)
      Shioya, Takashi
    • Organizer
      日中友好幾何学研究集会
    • Place of Presentation
      中国四川
    • Year and Date
      2012-09-11
    • Related Report
      2013 Final Research Report
  • [Presentation] 崩壊多様体に対するスペクトル逆問題2012

    • Author(s)
      山 口 孝男
    • Organizer
      偏微分方程式の逆問題解析 その周辺分野に関する 研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-01-23
    • Related Report
      2013 Final Research Report
  • [Presentation] Introduction to the spectral theory on generalized arithmetic surfaces2011

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      Inverse Days (University of Helsinki)
    • Place of Presentation
      Finnland
    • Year and Date
      2011-12-16
    • Related Report
      2013 Final Research Report
  • [Presentation] Collapsing manifolds and inverse spectral problems2011

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      Finnish -Japanese-Korean Workshop on Inverse Problems 2011
    • Place of Presentation
      University of Helsinki, Finland
    • Year and Date
      2011-12-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Collapsing manifolds and inverse spectral problems2011

    • Author(s)
      Takao Yamaguchi
    • Organizer
      Finnish-Japanese-Korean Workshop on Inverse Problems 2011
    • Place of Presentation
      University of Helsinki, Finland(招待講演)
    • Year and Date
      2011-12-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Inverse scattering from cusp on generalized arithmetic surfaces2011

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      Inverse Problems in Analysis and Geometry
    • Place of Presentation
      Issac Newton Institute, Cambridge, England
    • Year and Date
      2011-08-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Concentration, Ricci curvature, eigenvalues of Laplacian2011

    • Author(s)
      Shioya, Takashi
    • Organizer
      Metric Geometry and Applications
    • Place of Presentation
      中国南京
    • Year and Date
      2011-07-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse scattering on Generalized arithmetic surfaces2011

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      International conference on Harmonic analysis
    • Place of Presentation
      Tufts University, USA
    • Year and Date
      2011-01-09
    • Related Report
      2013 Final Research Report
  • [Presentation] Collapsing and essential coverings of Rimennian manifolds2010

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      The 6th Geometry Conference of friendship of China and Japan
    • Place of Presentation
      Xian, China
    • Year and Date
      2010-09-04
    • Related Report
      2013 Final Research Report
  • [Presentation] Collapsing and essential coverings2010

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      Japan-China Friendship Geometry Meeting
    • Place of Presentation
      Xian,China(招待講演)
    • Year and Date
      2010-09-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Reconstruction of collapsed manifolds2010

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      ICM2010
    • Place of Presentation
      Hyderabad, India
    • Year and Date
      2010-08-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Reconstruction of collapsed manifolds2010

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      International, Congress of Mathematicians 2010
    • Place of Presentation
      Hyderabad,India(招待講演)
    • Year and Date
      2010-08-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] A splitting theorem for weighted Alexandrov spaces2010

    • Author(s)
      Shioya, Takashi
    • Organizer
      日中友好幾何学研究集会
    • Place of Presentation
      沖縄市
    • Year and Date
      2010-01-31
    • Related Report
      2013 Final Research Report
  • [Presentation] リーマン面上での逆散乱問題2009

    • Author(s)
      磯崎洋
    • Organizer
      浜松偏微分方程式セミ ナー
    • Place of Presentation
      静岡大学
    • Year and Date
      2009-12-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse scattering from cusp2009

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      Paris-London Analysis Seminar
    • Place of Presentation
      L' Institute Henri Poincare, France
    • Year and Date
      2009-12-04
    • Related Report
      2013 Final Research Report
  • [Presentation] リーマン多様体の崩壊と本質的被覆2009

    • Author(s)
      山口 孝男
    • Organizer
      大岡山談話会
    • Place of Presentation
      東工大
    • Year and Date
      2009-12-02
    • Related Report
      2013 Final Research Report
  • [Presentation] Collapsing and essential covering of Rimennian manifolds2009

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      Colloquim, Univ of Notre Dam
    • Year and Date
      2009-11-04
    • Related Report
      2013 Final Research Report
  • [Presentation] Collapsing and essential coverings2009

    • Author(s)
      Yamaguchi, Takao
    • Organizer
      Collogium talk
    • Place of Presentation
      Univ of Notre Dum, VSA
    • Year and Date
      2009-11-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] Inverse scattering on non-compact manifolds2009

    • Author(s)
      Isozaki, Hiroshi
    • Organizer
      AIP Conference (Wien)
    • Place of Presentation
      オーストリア
    • Year and Date
      2009-07-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Geometric aspect of measure concentration2009

    • Author(s)
      Shioya, Takashi
    • Organizer
      研究会「保存則と幾何学的偏微分方程式とその応用」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-06-11
    • Related Report
      2013 Final Research Report
  • [Presentation] ラ ドン変換と波動方程式2009

    • Author(s)
      磯崎洋
    • Organizer
      中央大学 Encounter with Mathematics
    • Place of Presentation
      中央大学
    • Year and Date
      2009-05-30
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse spectral problems for collapsed manifolds

    • Author(s)
      山口孝男
    • Organizer
      Probability Theory and Geometry
    • Place of Presentation
      京都大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 崩壊とスペクトル逆問題

    • Author(s)
      山口孝男
    • Organizer
      第60回幾何学シンポジウム
    • Place of Presentation
      東京工業大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Collapsing three-dimensional Alexandrov spaces

    • Author(s)
      山口孝男
    • Organizer
      低次元多様体モジュライ空間の幾何
    • Place of Presentation
      京都大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 空間の集中・収束・消散

    • Author(s)
      塩谷隆
    • Organizer
      日本数学会企画特別講演
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] アレクサンドロフ空間の局所リプシッツ可縮性とその応用

    • Author(s)
      三石史人、山口孝男
    • Organizer
      日本数学会 2012 年度秋季総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
  • [Book] 重点解説基礎微分幾何2009

    • Author(s)
      塩谷 隆
    • Total Pages
      204
    • Publisher
      サイエンス社
    • Related Report
      2013 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

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