Fattening in mean curvature flow
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910903809605632 |
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| author | Ilmanen, Tom White, Brian |
| author_facet | Ilmanen, Tom White, Brian |
| contents | For each $g\ge 3$, we prove existence of a compact, connected, smoothly embedded, genus-$g$ surface $M_g$ with the following property: under mean curvature flow, there is exactly one singular point at the first singular time, and the tangent flow at the singularity is given by a shrinker with genus $(g-1)$ and with two ends. Furthermore, we show that if $g$ is sufficiently large, then $M_g$ fattens at the first singular time. As $g\to\infty$, the shrinker converges to a multiplicity $2$ plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fattening in mean curvature flow Ilmanen, Tom White, Brian Differential Geometry 53E10 For each $g\ge 3$, we prove existence of a compact, connected, smoothly embedded, genus-$g$ surface $M_g$ with the following property: under mean curvature flow, there is exactly one singular point at the first singular time, and the tangent flow at the singularity is given by a shrinker with genus $(g-1)$ and with two ends. Furthermore, we show that if $g$ is sufficiently large, then $M_g$ fattens at the first singular time. As $g\to\infty$, the shrinker converges to a multiplicity $2$ plane. |
| title | Fattening in mean curvature flow |
| topic | Differential Geometry 53E10 |
| url | https://arxiv.org/abs/2406.18703 |