As on arXiv
Abstract
In this paper, using heat kernel estimates and contraction mapping principle, we give a new proof of the existence and uniqueness of mean curvature flow starting from hypersurface with bounded second fundamental form. Moreover, we show the continuous dependence of mean curvature flow on initial data.
Comments: 21pages
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.
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The Ricci-DeTurck flow on complete manifolds
Topics Heat kernel, Stability & uniqueness · Shared terms “continuous dependence”, “kernel estimates”, “flow starting”
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Gaussian heat kernel estimates of Bamler-Zhang type along super Ricci flow
Topics Heat kernel · Shared terms “kernel estimates”
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Heat kernel on Ricci shrinkers (II)
Topics Heat kernel
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Topics Heat kernel
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The Fisher Metric of the Ricci Flow Heat Kernel
Topics Heat kernel, Stability & uniqueness · Shared terms “contraction”
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Perelman's entropy and heat kernel bounds on RCD spaces
Topics Heat kernel, Stability & uniqueness
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Pseudolocality of -Laplacian Flow
Topics Heat kernel, Stability & uniqueness · Shared terms “kernel estimates”, “dependence”
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.3The Heat Equation on ℝⁿ
The heat kernel, smoothing, uniqueness, Brownian motion, and a Gaussian that runs to Perelman.
- 6A.4Fourier Methods and Scale Space
Fourier's own method on the circle and the line, smoothing as the decay of high frequencies, and the heat equation as the mathematics of blurring images.
- 6A.12Entropy, Information and Diffusion
Entropy along the heat flow, the log-Sobolev inequality and Li–Yau: the ancestors of Perelman’s entropy.