Paper · Feb 4, 2022
The rate of -convergence for Ricci flows with closed and smooth tangent flows
As on arXiv
Abstract
This article is a continuation of [CMZ21b], where we proved that a Ricci flow with a closed and smooth tangent flow has unique tangent flow, and its corresponding forward or backward modified Ricci flow converges in the rate of for some . In this article, we calculate the corresponding -convergence rate: after being scaled by a factor , a Ricci flow with closed and smooth tangent flow is close to its tangent flow in the -sense, where is a positive number, in the blow-up case, and in the blow-down case.
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
On Ricci flows with closed and smooth tangent flows
Topics Singularities · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “smooth tangent”, “tangent flow”, “backward”
-
Rigidity and gap theorems for Ricci shrinkers
Topics Singularities · Same authors Pak-Yeung Chan, Yongjia Zhang
-
On noncollapsed -limit metric solitons
Topics Singularities · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
-
Dimension Reduction for Positively Curved Steady Solitons
Topics Singularities · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “tangent flow”
-
Lower bounds for the scalar curvatures of Ricci flow singularity models
Topics Singularities · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
-
Local smooth convergence of -limit flows
Topics Ricci flow · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
-
Hamilton-Ivey estimates for gradient Ricci solitons
Topics Singularities · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
-
A local Sobolev inequality on Ricci flow and its applications
Topics Ricci flow · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.4Blow-Ups, Blow-Downs and Splitting at Infinity
Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.
- 11B.6Rotationally Symmetric Flows and the Standard Solution
The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.
- 6A.13Self-Similar Variables and Monotonicity
Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.