A remark on the Gaussian lower bound for the Neumann heat kernel of the Laplace-Beltrami operator

TL;DR

This paper adapts a perturbation method to establish a Gaussian lower bound for the Neumann heat kernel associated with the Laplace-Beltrami operator on open subsets of compact Riemannian manifolds, advancing understanding of heat kernel estimates.

Contribution

It introduces a novel adaptation of the perturbation method to derive Gaussian lower bounds for Neumann heat kernels on Riemannian manifolds.

Findings

Established Gaussian lower bounds for Neumann heat kernels.

Extended the perturbation method to the setting of Riemannian manifolds.

Provided a framework for future heat kernel estimates on manifolds.

Abstract

We adapt in the present note the perturbation method introduced in [3] to get a Gaussian lower bound for the Neumann heat kernel of the Laplace-Beltrami operator on an open subset of a compact Riemannian manifold.