Nondegenerate neck pinches along the mean curvature flow
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914620109750272 |
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| author | Székelyhidi, Gábor |
| author_facet | Székelyhidi, Gábor |
| contents | We show that for generic smooth compact initial surfaces the mean curvature flow in $\mathbb{R}^3$ has spherical or nondegenerate neck pinch singularities at the first singular time. In particular the singularities at the first singular time are isolated in spacetime. As an application we give a new approach to constructing a mean curvature flow with surgery for smooth compact initial surfaces in $\mathbb{R}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11022 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nondegenerate neck pinches along the mean curvature flow Székelyhidi, Gábor Differential Geometry 53E10 We show that for generic smooth compact initial surfaces the mean curvature flow in $\mathbb{R}^3$ has spherical or nondegenerate neck pinch singularities at the first singular time. In particular the singularities at the first singular time are isolated in spacetime. As an application we give a new approach to constructing a mean curvature flow with surgery for smooth compact initial surfaces in $\mathbb{R}^3$. |
| title | Nondegenerate neck pinches along the mean curvature flow |
| topic | Differential Geometry 53E10 |
| url | https://arxiv.org/abs/2603.11022 |