Local derivative estimates for the heat equation coupled to the Ricci flow

TL;DR

This paper derives local derivative estimates for the heat equation coupled with Ricci flow and extends key geometric results to noncompact manifolds, enhancing understanding of Ricci flow behavior.

Contribution

It provides Shi-type local derivative estimates for the heat equation coupled with Ricci flow and extends distance distortion and pseudolocality results to noncompact manifolds.

Findings

Established local derivative estimates for coupled heat and Ricci flow.

Extended distance distortion estimates to noncompact manifolds.

Proved a backward pseudolocality theorem for noncompact Ricci flow.

Abstract

In this note we obtain local derivative estimates of Shi-type for the heat equation coupled to the Ricci flow. As applications, in part combining with Kuang's work, we extend some results of Zhang and Bamler-Zhang including distance distortion estimates and a backward pseudolocality theorem for Ricci flow on compact manifolds to the noncompact case.