• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Dirichlet space and analysis of harmonic map over the space of Gromov-Hausdorff limit spaces

Research Project

Project/Area Number 13640220
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KUWAE Kazuhiro  Yokohama City University, Graduate school of integrated Science, Associate Professor, 総合理学研究科, 助教授 (80243814)

Co-Investigator(Kenkyū-buntansha) OTSU Yukio  Kyushu University, Graduate School of Mathematics, Associate Professor, 数理学研究院, 助教授 (80233170)
SHIOYA Takashi  Tohoku University, Graduate School of Mathematics, Associate Professor, 大学院・理学研究科, 助教授 (90235507)
OGURA Yukio  Yokohama City University, faculty of Science and Engineering Saga University, Professor, 理工学部, 教授 (00037847)
MACHIGASHIRA Yoshiroh  Osaka Kyoiku University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00253584)
市田 良輔  横浜市立大学, 総合理学研究科, 教授 (10094294)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsDirichlet form / Harmonic map / Variational convergence / Asymtotic relation / Gamma convergence / Mosco convergence / CAT(0)-space / Gromov-Hausdorff convergence / Alexandrov spaces / Calabi s strong maximum principle / 加藤クラス / ハーディクラス / アレキサンドロフ空間 / ドリフト変換過程 / ソボレフ空間 / ファインマンカッツ公式 / ギルサノフ公式 / グロモハウスドルフ収束
Research Abstract

(1)The study of variational convergence over metric measured space : This result is a joint work with Professor Takashi Shioya, who is an associate professor of Graduate School of Mathematical Institute, Tohoku University. We introduce a notion called asymptotic relation over a direct sum of metric spaces, which includes the notion of Gromov-Hausdorff convergence as an example. We discuss several notions of functionals over it, for example, Gamma convergence, Mosco convergence and compact convergence and so on. We give a sufficient condition for the compact convergence of functionals. We also prove a sufficient condition for the convergence of resolvents of energy functionals over CAT(0)-spaces.
(2)The study on the stochastic representation of semigroups obtained from a non-symmetric perturbation : This study is a joint work with Professors P.J.Fitzsimmons, Z.Q.Chen and T.S.Zhang. Consider a symmetric regular Dirichlet form and the associated Hunt process admitting jumps of its sample paths. We consider a non-symmetric perturbation by use of locally square integrable martingale additive functionals and a continuous additive functional of finite variation. We prove that the corresponding semigroup has a stochastic representation in terms of time reverse operator on sample paths.
(3)The study of Calabis type strong maximum principle : We give a stochastic proof of an extension of E.Calabi's strong maximum principle in the framework of strong Feller diffusion processes associated with local regular semi-Dirichlet forms. Our results can be applicable to the Gromov-Hausedorff limit space over a family of compact Riemannian manifolds with uniform lower bounds of Ricci curvature and uniform bounds of diameter.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (41 results)

All Other

All Publications (41 results)

  • [Publications] K.Kuwae, T.Shioya: "Sobolev and Dirichlet spaces between metric spaces"Journal fur die reine und angewandt Mathematik. 555. 39-75 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kuwae, T.Shioya: "Convergence of spectral geometry structures : a functional analytic theory and its applications to spectral"Communications in analysis and geometry. 11. 599-673 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kuwae: "Conservativeness of diffusion processes with drift"Proceedings of the American Mathematical Society. 132. 2743-2751 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] P.J.Fitzsimmons, K.Kuwae: "Non-symmetric perturbations of symmetric Dirichlet forms"Jour.Funct.Anal. 208. 140-162 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Shioya: "Behavior of distant maximal geodesics in finitely connected complete two-dimensional Riemannian manifolds, II"Geom.Dedicata. 103. 1-32 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Shioya, T.Yamaguchi: "Volume collapsed three-manifolds under a lower curvature bound"Math.Ann.. (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Li, Y.Ogura: "A convergence theorem of fuzzy-valued martingales in the extended Hausdorff metric $H_\infty$"Fuzzy Sets and Systems. 135. 391-399 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Li, Y.Ogura, F.N.Proske, M.L.Puri: "Central limit theorems for generalized set-valued random variables"Jour.Math.Anal.Appl.. 285. 250-263 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Matsumoto, Y.Ogura: "Markov or non-Markov property of cM-X processes"Jour.Math.Soc.Japan. 56. 519-540 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Shiohama, T.Shioya, M.Tanaka: "The geometry of total curvature on complete open surfaces"Cambridge University Press, Cambridge Tracts in Mathematics, 159. 284 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kuwae, T.Shioya: "Sobolev and Dirichlet spaces between metric spaces"Journal fur die reine und angewandt Mathematik. 555. 39-75 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kuwae, T.Shioya: "Convegence of spectral geometry structures : a functional analytic theory and its applications to spectral"Communications in analysis and geometry. 11. 599-673 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kuwae: "Conservativeness of diffusion processes with drift"Proceedings of he American Mathematical Society. (to appear). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] J.Fitzsimmons, K.Kuwae: "Non-symmetric perturbations on symmetric Dirichlet forms"Jour.Funct.Anal. 208. 140-162 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Shioya: "Behavior of distant maximal geodesics in finitely connected complete two-dimensional Riemannian manifolds, II"Geom.Dedicata. 103. 1-32 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Shioya, T.Yamaguchi: "Volume collapsed three-manifolds under a lower curvature bound"Math.Ann.. (to appear). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Liand, Y.Ogura: "A convergence theorem of fuzzy-valued martingales in the extended Hausdorff metric $H_\infty$"Fuzzy Sets and Systems. 135. 391-399 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Liand, Y Ogura, F.N.Proske, M.L.Puri: "Central limit theorems for generalized set-valued random variables"Jour.Math.Anal.Appl.. 285. 250-263 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Matsumoto, Y.Ogura: "Markov or non-Markov property of cM-X processes"Jour.Math.Anal.Appl. 56(to appear). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Shiohama, T.Shioya, M.Tanaka: "The geometry of total curvature on complete open Surfaces"Cambridge Tracts in Mathematics(Cambridge University Press, Cambridge). 159. 1-284 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kuwae, T.Shioya: "Sobolev and Dirichlet spaces between metric spaces"Journal fur die reine und angewandt Mathematik. 555. 39-75 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Kuwae, T.Shioya: "Convergence of spectral structures : a functional analytic theory and its applications to spectral geometry"Communications in analysis and geometry. 11. 599-673 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Kuwae: "Conservativeness of diffusion processes with drift"Proceedings of the American Mathematical Society. 132. 2743-2751 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] P.J.Fitzsimmons, K.Kuwae: "Non-symmetric perturbations of symmetric Dirichlet forms"Jour.Funct.Anal. 208. 140-162 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] I.Shioya: "Behavior of distant maximal geodesics in finitely connected complete two-dimensional Riemannian manifolds, II"Geom.Dedicata. 103. 1-32 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Shioya, T.Yamaguchi: "Volume collapsed three-manifolds under a lower curvature bound"Math.Ann.. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Li, Y.Ogura: "A convergence theorem of fuzzy-valued martingales in the extended Hausdorff metric $H_\infty$"Fuzzy Sets and Systems. 135. 391-399 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Li, Y.Ogura, F.N.Proske, M.L.Puri: "Central limit theorems for generalized set-valued random variables"Jour.Math.Anal.Appl.. 285. 250-263 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Matsumoto, Y.Ogura: "Markov or non-Markov property of cM-X processes"Jour.Math.Soc.Japan. 56. 519-540 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Shiohama, T.Shioya, M.Tanaka: "The geometry of total curvature on complete open surfaces"Cambridge University Press, Cambridge Cambridge-tracts in Mathematics, 159. 284 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Kuwae: "Reflected Dirichlet forms and the uniqueness of Silverstein's extension"Potential Analysis. 16. 221-247 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Kuwae, T.Shioya: "Sobolev and Dirichlet spaces between metric spaces"Journal fur die reine und angewandt Mathematik. 555. 39-75 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Kuwae, T.Shioya: "Convergence of spectral structures : a functional analytic theory and its applications to spectral geometry"Communications in analysis and geometry. (印刷中). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Kuwae: "Conservativeness of diffusion processes with drift"Proceedings of the American Mathematical Society. (印刷中). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Ogura, M.Tomisaki, M.Tsuchiya: "Convergence of local type Dirichlet forms to a non-local type one"Ann.Inst.H.Poincare Probab.Statist.. 38. 507-556 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Kuwae, T.Shioya: "On generalized measure contraction property and energy functionals over Lipschitz maps"Potential Analysis. 15. 105-121 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Kuwae, Y.Machigashira, T.Shioya: "Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces"Mathematische Zeitschrift. 238. 269-316 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Kuwae: "Reflected Dirichlet forms and the uniqueness of Silverstein s extension"Potential Analysis. 16. 221-247 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Shioya, T.Yamaguchi: "Collapsing three-manifolds under a lower curvature bound"J. Differential Geom. 56. 1-66 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Ogura: "Weak convergence of laws of stochastic processes on Riemannian manifolds"Probab. Theory Related Fields. 119. 529-557 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Machigashira, F.Otsuka: "Total excess on length surfaces"Math. Annalen. 319. 675-706 (2001)

    • Related Report
      2001 Annual Research Report

URL: 

Published: 2001-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi