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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Accesso online: | https://arxiv.org/abs/2210.00419 |
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| _version_ | 1866909753073991680 |
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| author | Sun, Ao Xue, Jinxin |
| author_facet | Sun, Ao Xue, Jinxin |
| contents | This paper studies the dynamics of mean curvature flow as it approaches a cylindrical singularity. We proved that the rescaled mean curvature flow converging to a smooth generalized cylinder can be written as a graph over the cylinder in a ball of radius $K\sqrt{t}$, and a normal form of the asymptotics. Using the normal form, we can define the nondegeneracy of cylindrical singularities, and we show that nondegenerate cylindrical singularities are isolated in space, have a mean convex neighborhood, and are type-I. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00419 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy Sun, Ao Xue, Jinxin Differential Geometry Analysis of PDEs Dynamical Systems 53E10, 37D10, 35J70, 35K65 This paper studies the dynamics of mean curvature flow as it approaches a cylindrical singularity. We proved that the rescaled mean curvature flow converging to a smooth generalized cylinder can be written as a graph over the cylinder in a ball of radius $K\sqrt{t}$, and a normal form of the asymptotics. Using the normal form, we can define the nondegeneracy of cylindrical singularities, and we show that nondegenerate cylindrical singularities are isolated in space, have a mean convex neighborhood, and are type-I. |
| title | Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy |
| topic | Differential Geometry Analysis of PDEs Dynamical Systems 53E10, 37D10, 35J70, 35K65 |
| url | https://arxiv.org/abs/2210.00419 |