Spectral gap on Riemannian path space over static and evolving manifolds
by Li-Juan Cheng and Anton Thalmaier

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 


The paper is available here:

Li Juan Cheng
Anton Thalmaier

Back to Homepage