On Generalized Measure Contraction Property and Energy Functional over Lipschitz Maps

Kazuhiro Kuwae, Takashi Shioya

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

We construct Sobolev spaces and energy functionals over maps between metric spaces under the strong measure contraction property of Bishop-Gromov type, which is a generalized notion of Ricci curvature bounded below. We also present the notion of generalized measure contraction property, which gives a characterization of energies by approximating energies of Sturm type over Lipschitz maps.

Original languageEnglish
Pages (from-to)105-121
Number of pages17
JournalPotential Analysis
Volume15
Issue number1-2
DOIs
Publication statusPublished - 2001

Keywords

  • Alexandrov space
  • Bishop inequality
  • Bishop-Gromov inequality
  • Dirichlet space
  • Harmonic map
  • Measure contraction property
  • Riemannian manifold
  • Sobolev space
  • Subpartitional lemma
  • Γ-limit

ASJC Scopus subject areas

  • Analysis

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