Reference : Spectral gap on Riemannian path space over static and evolving manifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/28889
Spectral gap on Riemannian path space over static and evolving manifolds
English
Cheng, Li Juan mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
15-Feb-2018
Journal of Functional Analysis
Academic Press
274
4
959-984
Yes (verified by ORBilu)
International
0022-1236
1096-0783
[en] Spectral gap ; path space ; Malliavin Calculus ; Ornstein-Uhlenbeck operator ; Ricci curvature ; geometric flow
[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.
Researchers ; Professionals
http://hdl.handle.net/10993/28889
10.1016/j.jfa.2017.12.004
http://doi.org/10.1016/j.jfa.2017.12.004
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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