Some Estimates of Fundamental Solution on noncompact manifolds with time-dependent metrics

TL;DR

This paper provides new estimates for fundamental solutions on noncompact manifolds with time-dependent metrics, extending previous results and exploring their asymptotic behaviors.

Contribution

It introduces improved estimates of fundamental solutions on noncompact manifolds with evolving metrics, advancing understanding of their asymptotic properties.

Findings

New estimates of fundamental solutions on noncompact manifolds

Applications to asymptotic behavior analysis

Extension of previous results by Chau-Tam-Yu

Abstract

In this article, we obtain some further estimates of fundamental solutions comparing to the result of Chau-Tam-Yu and give some applications of the estimates on asymptotic behaviors of fundamental solutions.