Mean curvature flow with generic initial data
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
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| _version_ | 1866911821739327488 |
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| author | Chodosh, Otis Choi, Kyeongsu Mantoulidis, Christos Schulze, Felix |
| author_facet | Chodosh, Otis Choi, Kyeongsu Mantoulidis, Christos Schulze, Felix |
| contents | We show that the mean curvature flow of generic closed surfaces in $\mathbb{R}^{3}$ avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in $\mathbb{R}^{4}$ is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_14344 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Mean curvature flow with generic initial data Chodosh, Otis Choi, Kyeongsu Mantoulidis, Christos Schulze, Felix Differential Geometry Analysis of PDEs We show that the mean curvature flow of generic closed surfaces in $\mathbb{R}^{3}$ avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in $\mathbb{R}^{4}$ is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons. |
| title | Mean curvature flow with generic initial data |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2003.14344 |