Remarks on spectral gaps on the Riemannian path space

2015/08/31 by Shizan Fang, Bo Wu, Fang, Shizan +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.PR #msc:60D05

paper · pdf · doi:10.48550/arxiv.1508.07657

arxiv created 2015/08/31 · arxiv updated 2015/09/01

Abstract

In this paper, we will give some remarks on links between the spectral gap of the Ornstein-Uhlenbeck operator on the Riemannian path space with lower and upper bounds of the Ricci curvature on the base manifold; this work was motivated by a recent work of A. Naber on the characterization of the bound of the Ricci curvature by analysis of path spaces.

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