As on arXiv
Abstract
The metric flow is introduced and extensively studied by Bamler [Bam20b, Bam20c], especially as an -limit of a sequence of smooth Ricci flows with uniformly bounded Nash entropy, in which case each regular point on the limit is a point of smooth convergence. In this note, we shall consider the -convergence of a sequence of -limit flows, and, like Bamler, show that each regular point on the limit is also a point of smooth convergence. The main result will be applied in a forthcoming work of the authors [CMZ23].
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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 Sobolev inequality on Ricci flow and its applications
Topics Perelman entropy · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “Nash entropy”
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Topics Ricci flow · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “smooth Ricci”
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Topics Ricci flow · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “Bamler”
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Topics Ricci flow · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
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Lower bounds for the scalar curvatures of Ricci flow singularity models
Topics Ricci flow · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “Bamler”
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A local gap theorem for Ricci shrinkers
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
- 6A.12Entropy, Information and Diffusion
Entropy along the heat flow, the log-Sobolev inequality and Li–Yau: the ancestors of Perelman’s entropy.
- 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.
- 6B.16Eigenvalue Problems and Perelman’s λ
Rayleigh quotients and min–max, Faber–Krahn and Cheeger’s inequality, ground states of Schrödinger operators, spectral clustering, and the first eigenvalue of −4Δ + R that begins Perelman’s first preprint.