Harmonic Functions, Entropy, and a Characterization of the Hyperbolic Space
نویسندگان
چکیده
منابع مشابه
Harmonic Functions, Entropy, and a Characterization of the Hyperbolic Space
Let (Mn; g) be a compact Riemannian manifold with Ric (n 1). It is well known that the bottom of spectrum 0 of its unverversal covering satis es 0 (n 1) =4. We prove that equality holds i¤ M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy. 1. Introduction Complete Riemannian manifolds with nonnegative Ricci curvature have been intensively studied by many people and...
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2007
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-007-9001-z