Spectral gap on
Riemannian path space over static and evolving manifolds
by Li-Juan Cheng and Anton Thalmaier
Abstract
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.
Journal of Functional Analysis 274 (2018) 659-984
https://doi.org/10.1016/j.jfa.2017.12.004
The paper is available here:
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