On Ricci flows with closed and smooth tangent flows
Abstract
In this paper, we consider Ricci flows admitting closed and smooth tangent flows in the sense of Bamler [Bam20c]. The tangent flow in question can be either a tangent flow at infinity for an ancient Ricci flow, or a tangent flow at a singular point for a Ricci flow developing a finite-time singularity. Among other things, we prove: (1) that in these cases the tangent flow must be unique, (2) that if a Ricci flow with finite-time singularity has a closed singularity model, then the singularity is of Type I and the singularity model is the tangent flow at the singular point; this answers a question proposed in [CCGGIIKLLN10], (3) a dichotomy theorem that characterizes ancient Ricci flows admitting a closed and smooth backward sequential limit.
Keywords
Cite
@article{arxiv.2109.14763,
title = {On Ricci flows with closed and smooth tangent flows},
author = {Pak-Yeung Chan and Zilu Ma and Yongjia Zhang},
journal= {arXiv preprint arXiv:2109.14763},
year = {2021}
}