Entropy in a Closed Manifold and Partial Regularity of Mean Curvature Flow Limit of Surfaces
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12220_2020_494_ReferencePDF.pdf
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Author(s)
Sun, Ao
Date Issued
August 11, 2020
Publisher
Springer US
Citation
Sun, Ao. 2020. "Entropy in a Closed Manifold and Partial Regularity of Mean Curvature Flow Limit of Surfaces."
Version
Author's final manuscript
Abstract
Abstract
Inspired by the idea of Colding and Minicozzi (Ann Math 182:755–833, 2015), we define (mean curvature flow) entropy for submanifolds in a general ambient Riemannian manifold. In particular, this entropy is equivalent to area growth of a closed submanifold in a closed ambient manifold with non-negative Ricci curvature. Moreover, this entropy is monotone along the mean curvature flow in a closed Riemannian manifold with non-negative sectional curvatures and parallel Ricci curvature. As an application, we show the partial regularity of the limit of mean curvature flow of surfaces in a three dimensional Riemannian manifold with non-negative sectional curvatures and parallel Ricci curvature.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s12220-020-00494-z
