A note on convergence of noncompact nonsingular solutions of the Ricci flow

TL;DR

This paper extends convergence results of nonsingular Ricci flows from compact to certain noncompact cases and shows that blow-up limits at finite time singularities are gradient shrinking solitons.

Contribution

It generalizes convergence results to infinite volume noncompact Ricci flows that are partially nonsingular and characterizes blow-up limits at certain singularities.

Findings

Extended convergence results to noncompact Ricci flows.

Proved blow-up limits at certain singularities are gradient shrinking solitons.

Connected partial nonsingularity with the formation of singularities.

Abstract

We extend some convergence results on nonsingular compact Ricci flows in the papers \cite{Ha:1}, \cite{Se:1} and \cite{FZZ:2} to certain infinite volume noncompact cases which are "partially" nonsingular. As an application, for a finite time singularity which is partially type I, it is shown that a blow up limit is a gradient shrinking soliton.