Article (Scientific journals)
Spectral gap on Riemannian path space over static and evolving manifolds
Cheng, Li Juan; Thalmaier, Anton
2018In Journal of Functional Analysis, 274 (4), p. 959-984
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Keywords :
Spectral gap; path space; Malliavin Calculus; Ornstein-Uhlenbeck operator; Ricci curvature; geometric flow
Abstract :
[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
Publication date :
15 February 2018
Journal title :
Journal of Functional Analysis
ISSN :
1096-0783
Publisher :
Academic Press
Volume :
274
Issue :
4
Pages :
959-984
Peer reviewed :
Peer Reviewed verified by ORBi
FnR Project :
FNR7628746 - Geometry Of Random Evolutions, 2014 (01/03/2015-28/02/2018) - Anton Thalmaier
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