[en] In this article, we continue the discussion of Fang–Wu (2015) to estimate the spectral gap of the Ornstein–Uhlenbeck operator on path space over a Riemannian manifold of pinched Ricci curvature. Along with explicit estimates we study the short-time asymptotics of the spectral gap. The results are then extended to the path space of Riemannian manifolds evolving under a geometric flow. Our paper is strongly motivated by Naber’s recent work (2015) on characterizing bounded Ricci curvature through stochastic analysis on path space.
Disciplines :
Mathematics
Author, co-author :
CHENG, Li Juan ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
THALMAIER, Anton ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Spectral gap on Riemannian path space over static and evolving manifolds
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