Mean Curvature Flow from Conical Singularities
| Autor: | Chodosh, Otis, Daniels-Holgate, J. M., Schulze, Felix |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove Ilmanen's resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities and resolves a particular case of Ilmanen's strict genus reduction conjecture. Precisely, we prove that the level set flow of a smooth hypersurface $M^n\subset \mathbb{R}^{n+1}$, $2\leq n\leq 6$, with an isolated conical singularity is modeled on the level set flow of the cone. In particular, the flow fattens (instantaneously) if and only if the level set flow of the cone fattens. Comment: 22 pages, 3 figures. Comments welcome! |
| Databáze: | arXiv |
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