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：
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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.
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页码：272 / 284
页数：12
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