On some strong ratio limit theorems for heat kernels

TL;DR

This paper investigates the asymptotic behavior of heat kernel ratios on noncompact Riemannian manifolds, focusing on subcritical and critical operators, to establish strong ratio limit theorems.

Contribution

It provides new strong ratio limit theorems for heat kernel quotients associated with subcritical and critical operators on noncompact manifolds.

Findings

Established strong ratio limit theorems for heat kernels

Analyzed behavior of heat kernel quotients in different operator regimes

Extended understanding of heat kernel asymptotics on manifolds

Abstract

We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.