Singularity of mean curvature flow with bounded mean curvature and Morse index
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912254661754880 |
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| author | Han, Yongheng |
| author_facet | Han, Yongheng |
| contents | We study the multiplicity of the singularity of mean curvature flow with bounded mean curvature and Morse index. For $3\leq n\leq 6$, we show that either the mean curvature or the Morse index blows up at the first singular time for a closed smooth embedded mean curvature flow in $\mathbb{R}^{n+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularity of mean curvature flow with bounded mean curvature and Morse index Han, Yongheng Differential Geometry 53E10 We study the multiplicity of the singularity of mean curvature flow with bounded mean curvature and Morse index. For $3\leq n\leq 6$, we show that either the mean curvature or the Morse index blows up at the first singular time for a closed smooth embedded mean curvature flow in $\mathbb{R}^{n+1}$. |
| title | Singularity of mean curvature flow with bounded mean curvature and Morse index |
| topic | Differential Geometry 53E10 |
| url | https://arxiv.org/abs/2501.05489 |