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 |
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Springer US,
2021-10-29T18:31:29Z.
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| Online Access: | Get fulltext |
| LEADER | 01089 am a22001333u 4500 | ||
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| 001 | 136747 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Sun, Ao |e author |
| 245 | 0 | 0 | |a Entropy in a Closed Manifold and Partial Regularity of Mean Curvature Flow Limit of Surfaces |
| 260 | |b Springer US, |c 2021-10-29T18:31:29Z. | ||
| 856 | |z Get fulltext |u https://hdl.handle.net/1721.1/136747 | ||
| 520 | |a 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. | ||
| 546 | |a en | ||
| 655 | 7 | |a Article | |