On generalized measure contraction property and energy functionals over Lipschitz maps

被引：23

作者：

Kuwae, K ^{[1
]}

Shioya, T

机构：

[1] Yokohama City Univ, Dept Math Sci, Yokohama, Kanagawa 2360027, Japan

[2] Tohoku Univ, Inst Math, Semdai 9808578, Japan

来源：

POTENTIAL ANALYSIS | 2001年 / 15卷 / 1-2期

关键词：

Dirichlet space; Sobolev space; measure contraction property; subpartitional lemma; Gamma-limit; Riemannian manifold; Alexandrov space; harmonic map; Bishop inequality; Bishop-Gromov inequality;

D O I：

10.1023/A:1011218425271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：105 / 121

页数：17

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