Sharp Entropy Bounds for Self-Shrinkers in Mean Curvature Flow
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866909148222849024 |
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| author | Hershkovits, Or White, Brian |
| author_facet | Hershkovits, Or White, Brian |
| contents | Let $M\subset {\mathbf R}^{m+1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial $k^{\rm th}$ homology. We show that the entropy of $M$ is greater than or equal to the entropy of a round $k$-sphere, and that if equality holds, then $M$ is a round $k$-sphere in ${\mathbf R}^{k+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_00637 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Sharp Entropy Bounds for Self-Shrinkers in Mean Curvature Flow Hershkovits, Or White, Brian Differential Geometry Primary 53C44, Secondary 49Q20 Let $M\subset {\mathbf R}^{m+1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial $k^{\rm th}$ homology. We show that the entropy of $M$ is greater than or equal to the entropy of a round $k$-sphere, and that if equality holds, then $M$ is a round $k$-sphere in ${\mathbf R}^{k+1}$. |
| title | Sharp Entropy Bounds for Self-Shrinkers in Mean Curvature Flow |
| topic | Differential Geometry Primary 53C44, Secondary 49Q20 |
| url | https://arxiv.org/abs/1803.00637 |