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

理学研究科・数学専攻

研究成果: Article › 査読

22 被引用数 (Scopus)

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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.

本文言語	English
ページ（範囲）	105-121
ページ数	17
ジャーナル	Potential Analysis
巻	15
号	1-2
DOI	https://doi.org/10.1023/A:1011218425271
出版ステータス	Published - 2001

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author = "Kazuhiro Kuwae and Takashi Shioya",

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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 - 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

KW - Γ-limit

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DO - 10.1023/A:1011218425271

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JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

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ER -

On Generalized Measure Contraction Property and Energy Functional over Lipschitz Maps

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