Entropy in a Closed Manifold and Partial Regularity of Mean Curvature Flow Limit of Surfaces
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 n...
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| Format: | Article |
| Language: | English |
| Published: |
Springer US,
2021-10-29T18:31:29Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | 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. |
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