Remarks on spectral gaps on the Riemannian path space

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.

References in corpus (1)

• Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth Spaces

Cited by in corpus (3)

• Pointwise Characterizations of Curvature and Second Fundamental Form on Riemannian Manifolds
• Characterizations of the upper bound of Bakry-Emery curvature
• Spectral gap on Riemannian path space over static and evolving manifolds