Harmonic Functions, Entropy, and a Characterization of the Hyperbolic Space

被引：0

作者：

Xiaodong Wang

机构：

[1] Michigan State University,Department of Mathematics

来源：

Journal of Geometric Analysis | 2008年 / 18卷

关键词：

Harmonic functions; Entropy; spectrum; 53C24; 31C05; 58J50;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let (Mn,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ0 of its universal covering satisfies λ0≤(n−1)2/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy.

引用

页码：272 / 284

页数：12

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