Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Gradient Estimates of Harmonic Functions and the Asymptotics of Spectral Gaps on Path Spaces
Shigeki AIDA
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1996 Volume 2 Issue 1 Pages 75-84

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Abstract
We show that the spectral gap of the Dirichlet form on the path space Px (M )T =C ([0,T ]→M ; γ(0)=x ) goes to 0 exponentially, when T → ∞. Here, M is a compact negatively curved manifold. This contrasts with the case of positive curvature. It is proved by using a gradient estimate of bounded harmonic functions on negatively curved manifolds.
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© 1996 by the Graduate School of Information Sciences (GSIS), Tohoku University

This article is licensed under a Creative Commons [Attribution 4.0 International] license.
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