A REFINEMENT OF GUNTHER'S CANDLE INEQUALITY

被引：3

作者：

Kloeckner, Benoit R. ^{[1
,2
]}

Kuperberg, Greg ^{[3
]}

机构：

[1] Univ Grenoble Alpes, IF, F-38000 Grenoble, France

[2] CNRS, IF, F-38000 Grenoble, France

[3] Univ Calif Davis, Dept Math, Davis, CA 95616 USA

来源：

ASIAN JOURNAL OF MATHEMATICS | 2015年 / 19卷 / 01期

基金：

美国国家科学基金会;

关键词：

Gunther-Bishop Theorem; Riemannian manifold; Ricci curvature; candle function; volume bounds; curvature bounds; MEASURE THEORETIC ENTROPY; GEODESIC-FLOWS; TOPOLOGICAL-ENTROPY; RICCI CURVATURE;

D O I：

10.4310/AJM.2015.v19.n1.a5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze an upper bound on the curvature of a Riemannian manifold, using. "root Ric" curvature, which is in between a sectional curvature bound and a Ricci curvature bound. (A special case of root Ric curvature was previously discovered by Osserman and Sarnak for a different but related purpose.) We prove that our root Ric bound implies Gunther's inequality on the candle function of a manifold, thus bringing that inequality closer in form to the complementary inequality due to Bishop.

引用

页码：121 / 134

页数：14

共 19 条

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