A heat kernel characterization of asymptotic harmonicity

Ledrappier, François

doi:10.1090/S0002-9939-1993-1137226-4

A heat kernel characterization of asymptotic harmonicity
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Proc. Amer. Math. Soc. 118 (1993), 1001-1004 Request permission

Abstract:

A compact negatively curved manifold is asymptotically harmonic if and only if the relation $4{\lambda _1} = \beta$ holds, where ${\lambda _1}$ is the spectral gap of the Laplacian on the universal cover, and $\beta$ is the Kaimanovich entropy.

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