Singularities of Mean Curvature Flow of Surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910004347404288 |
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| author | Ilmanen, Tom |
| author_facet | Ilmanen, Tom |
| contents | This paper proves that, at the first singular time for a smoothly immersed surface moving by mean curvature flow in a n-manifold, each tangent flow is given by a smooth, branched shrinker, possibly with multiplicity. If n=3 and if the initial surface is embedded, then the shrinker is smoothly embedded without branch points, but possibly with multiplicity. A key ingredient of the proof is a new, local version of the Gauss-Bonnet formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21133 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singularities of Mean Curvature Flow of Surfaces Ilmanen, Tom Differential Geometry 53E10 This paper proves that, at the first singular time for a smoothly immersed surface moving by mean curvature flow in a n-manifold, each tangent flow is given by a smooth, branched shrinker, possibly with multiplicity. If n=3 and if the initial surface is embedded, then the shrinker is smoothly embedded without branch points, but possibly with multiplicity. A key ingredient of the proof is a new, local version of the Gauss-Bonnet formula. |
| title | Singularities of Mean Curvature Flow of Surfaces |
| topic | Differential Geometry 53E10 |
| url | https://arxiv.org/abs/2601.21133 |