As on arXiv
Abstract
We prove local versions of the Ricci curvature and -entropy gap theorems for Ricci shrinkers, which respectively generalize a previous result of Munteanu-Wang and a prior result of the authors with Ma. The key point is that these local gaps depend only on the dimension and not on the global entropy or any other geometric information of the Ricci shrinker. As an application, we provide a local criterion for removable Type I singularities of the Ricci flow.
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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.
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A local gap theorem for Ricci shrinkers
Topics Ricci solitons · Same authors Pak-Yeung Chan, Yongjia Zhang · Shared terms “gap theorem”, “local gap”, “Ricci shrinkers”
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On noncollapsed -limit metric solitons
Topics Singularities, Ricci solitons · Same authors Pak-Yeung Chan, Yongjia Zhang · Shared terms “gap theorem”, “local gap”, “Ricci shrinkers”
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A gap theorem for metric solitons and its applications
Topics Singularities · Same author Yongjia Zhang · Shared terms “gap theorem”, “Wang”
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On Ricci flows with closed and smooth tangent flows
Topics Singularities · Same authors Pak-Yeung Chan, Yongjia Zhang
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Lower bounds for the scalar curvatures of Ricci flow singularity models
Topics Singularities, Ricci solitons · Same authors Pak-Yeung Chan, Yongjia Zhang
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Dimension Reduction for Positively Curved Steady Solitons
Topics Singularities, Ricci solitons · Same authors Pak-Yeung Chan, Yongjia Zhang
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The rate of -convergence for Ricci flows with closed and smooth tangent flows
Topics Singularities · Same authors Pak-Yeung Chan, Yongjia Zhang
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A local Sobolev inequality on Ricci flow and its applications
Topics Ricci flow · Same authors Pak-Yeung Chan, 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.