On Generalized Measure Contraction Property and Energy Functional over Lipschitz Maps

Kazuhiro Kuwae; Takashi Shioya

doi:10.1023/A:1011218425271

On Generalized Measure Contraction Property and Energy Functional over Lipschitz Maps

Kazuhiro Kuwae, Takashi Shioya

SCI - Mathematics

Yokohama City University

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	105-121
Number of pages	17
Journal	Potential Analysis
Volume	15
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1011218425271
Publication status	Published - 2001

Keywords

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

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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.",

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AU - Shioya, Takashi

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AB - 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.

KW - Γ-limit

KW - Alexandrov space

KW - Bishop inequality

KW - Bishop-Gromov inequality

KW - Dirichlet space

KW - Harmonic map

KW - Measure contraction property

KW - Riemannian manifold

KW - Sobolev space

KW - Subpartitional lemma

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VL - 15

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JO - Potential Analysis

JF - Potential Analysis

IS - 1-2

ER -

On Generalized Measure Contraction Property and Energy Functional over Lipschitz Maps

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Keywords

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