Harmonic Functions,Entropy, and a Characterization of the Hyperbolic Space |
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| Authors: | Xiaodong Wang |
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| Affiliation: | (1) Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA |
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| Abstract: | Let (M n ,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ 0 of its universal covering satisfies λ 0≤(n−1)2/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy. The author was partially supported by NSF Grant 0505645. |
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| Keywords: | Harmonic functions Entropy L 2 spectrum |
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