  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.
