Two-sided estimates of heat kernels on metric measure spaces

TL;DR

This paper establishes conditions under which heat kernels on metric measure spaces satisfy two-sided sub-Gaussian estimates, advancing understanding of heat distribution in complex geometric contexts.

Contribution

It provides new equivalent conditions for two-sided sub-Gaussian heat kernel estimates on metric measure spaces.

Findings

Derived necessary and sufficient conditions for heat kernel estimates

Unified framework for sub-Gaussian heat kernel bounds

Applicable to a broad class of metric measure spaces

Abstract

We prove equivalent conditions for two-sided sub-Gaussian estimates of heat kernels on metric measure spaces.