Title: Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds

Authors: Hajime Urakawa

Issue: Volume 55 (2006), Issue 1, 259-288

Abstract: In this paper, we show Lipschitz continuity of the convergence rate to the equilibrium of the heat kernels with respect to the spectral distance on the space of all compact Riemannian manifolds, and several comparison theorems of the convergence rates of the heat kernels on compact Riemannian manifolds in terms of the infimum of the Ricci curvature, and Riemannian submersions, and show the estimates of the precise convergence rates for compact rank one symmetric spaces. We also show the convergence rates of the Neumann heat kernels for the Euclidean domains and the spherical domains.