Mean curvature flow converging to an minimizing cone and its Hardt-Simon foliation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915550672715776 |
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| author | Huang, Jiuzhou |
| author_facet | Huang, Jiuzhou |
| contents | In this paper, we construct a family of mean curvature flow which converges to an area minimizing, strictly stable hypercone $\mC$ after type I rescaling, and converges to the Hardt-Simon foliation of the cone after a type II rescaling provided the cone satisfies some technique conditions. The difference from Velázquez's previous results is that we drop the symmetry condition on the cone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean curvature flow converging to an minimizing cone and its Hardt-Simon foliation Huang, Jiuzhou Differential Geometry In this paper, we construct a family of mean curvature flow which converges to an area minimizing, strictly stable hypercone $\mC$ after type I rescaling, and converges to the Hardt-Simon foliation of the cone after a type II rescaling provided the cone satisfies some technique conditions. The difference from Velázquez's previous results is that we drop the symmetry condition on the cone. |
| title | Mean curvature flow converging to an minimizing cone and its Hardt-Simon foliation |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.11430 |