Spectral gap on Riemannian path space over static and evolving manifolds

Li-Juan Cheng; Anton Thalmaier

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arXiv · 1611.02165

Spectral gap on Riemannian path space over static and evolving manifolds

Li-Juan Cheng·Anton Thalmaier

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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.

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Li-Juan Cheng, Anton Thalmaier. 2016-11-07. Spectral gap on Riemannian path space over static and evolving manifolds. https://arxiv.org/abs/1611.02165

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