# Spectral gaps for the O-U/Stochastic heat processes on path space over a Riemannian manifold with boundary

## TL;DR

This paper extends spectral gap results for Ornstein-Uhlenbeck and stochastic heat processes on path spaces from boundaryless to bounded Riemannian manifolds, broadening understanding of these processes in more general geometric settings.

## Contribution

It introduces spectral gap estimates for these processes on manifolds with boundary, a significant generalization of prior boundaryless results.

## Key findings

- Spectral gap estimates for O-U process on manifolds with boundary
- Spectral gap estimates for stochastic heat process on manifolds with boundary
- Extension of previous results to new geometric setting

## Abstract

Fang-Wu\cite{FW17} presented a explicit spectral gap for the O-U process on path space over a Riemannian manifold without boundary under the bounded Ricci curvature conditions. In this paper, we will extend these results to the case of the Riemannian manifold with boundary. Moreover, we also derive the similar results for the stochastic heat process.