Generic regularity of Level Set Flows with spherical singularity
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909143850287104 |
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| author | Sun, Ao Xue, Jinxin |
| author_facet | Sun, Ao Xue, Jinxin |
| contents | The sphere is well-known as the only generic compact shrinker for mean curvature flow (MCF). In this paper, we characterize the generic dynamics of MCFs with a spherical singularity. In terms of the level set flow formulation of MCF, we establish that generically the arrival time function of level set flow with spherical singularity has at most $C^2$ regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_07896 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generic regularity of Level Set Flows with spherical singularity Sun, Ao Xue, Jinxin Differential Geometry Analysis of PDEs Dynamical Systems 53E10, 37D10, 35J70, 35K65 The sphere is well-known as the only generic compact shrinker for mean curvature flow (MCF). In this paper, we characterize the generic dynamics of MCFs with a spherical singularity. In terms of the level set flow formulation of MCF, we establish that generically the arrival time function of level set flow with spherical singularity has at most $C^2$ regularity. |
| title | Generic regularity of Level Set Flows with spherical singularity |
| topic | Differential Geometry Analysis of PDEs Dynamical Systems 53E10, 37D10, 35J70, 35K65 |
| url | https://arxiv.org/abs/2204.07896 |