Closed embedded self-shrinkers of mean curvature flow
| Autor: | Riedler, Oskar |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Geometric Analysis 33, 172 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s12220-023-01217-w |
| Popis: | In this article we show the existence of closed embedded self-shrinkers in $\Bbb{R}^{n+1}$ that are topologically of type $S^1\times M$, where $M\subset S^n$ is any isoparametric hypersurface in $S^n$ for which the multiplicities of the principle curvatures agree. This yields new examples of closed self-shrinkers, for example self-shrinkers of topological type $S^1\times S^k\times S^k\subset \Bbb R^{2k+2}$ for any $k$. If the number of distinct principle curvatures of $M$ is one the resulting self-shrinker is topologically $S^1\times S^{n-1}$ and the construction recovers Angenent's shrinking doughnut. Comment: 31 pages, 3 figures |
| Databáze: | arXiv |
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