Revisiting generic mean curvature flow in $\mathbb{R}^3$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914080895270912 |
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| author | Chodosh, Otis Choi, Kyeongsu Mantoulidis, Christos Schulze, Felix |
| author_facet | Chodosh, Otis Choi, Kyeongsu Mantoulidis, Christos Schulze, Felix |
| contents | Bamler--Kleiner recently proved a multiplicity-one theorem for mean curvature flow in R^3 and combined it with the authors' work on generic mean curvature flows to fully resolve Huisken's genericity conjecture. In this paper we show that a short density-drop theorem plus the Bamler--Kleiner multiplicity-one theorem for tangent flows at the first nongeneric singular time suffice to resolve Huisken's conjecture -- without relying on the strict genus drop theorem for one-sided ancient flows previously established by the authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting generic mean curvature flow in $\mathbb{R}^3$ Chodosh, Otis Choi, Kyeongsu Mantoulidis, Christos Schulze, Felix Differential Geometry Bamler--Kleiner recently proved a multiplicity-one theorem for mean curvature flow in R^3 and combined it with the authors' work on generic mean curvature flows to fully resolve Huisken's genericity conjecture. In this paper we show that a short density-drop theorem plus the Bamler--Kleiner multiplicity-one theorem for tangent flows at the first nongeneric singular time suffice to resolve Huisken's conjecture -- without relying on the strict genus drop theorem for one-sided ancient flows previously established by the authors. |
| title | Revisiting generic mean curvature flow in $\mathbb{R}^3$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2409.01463 |