Heat kernel on Ricci shrinkers (II)

TL;DR

This paper advances the understanding of heat kernels on Ricci shrinkers by refining estimates, removing previous assumptions, and establishing the natural applicability of $ ext{IF}$-convergence in Ricci flows induced by Ricci shrinkers.

Contribution

It improves existing estimates, extends recent progress, and demonstrates the natural occurrence of $ ext{IF}$-convergence without compactness or curvature bounds.

Findings

Refined heat kernel estimates on Ricci shrinkers.

Extended $ ext{IF}$-convergence theory to non-compact Ricci flows.

Removed assumptions of compactness and bounded curvature.

Abstract

This paper is the sequel to our study of heat kernels on Ricci shrinkers in \cite{LW20}. In this paper, we improve many estimates in \cite{LW20} and extend the recent progress of Bamler \cite{Bam20a}. In particular, we drop the compactness and curvature boundedness assumptions and show that the theory of $\IF$-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.