Convexity of 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$
| Autor: | Xie, Junming, Yu, Jiangtao |
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| Rok vydání: | 2022 |
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| Zdroj: | J. Geom. Anal. 33 (2023), no. 8, Paper No. 252, 19 pp |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s12220-023-01260-7 |
| Popis: | In this paper, inspired by the work of Spruck-Xiao [27] and based partly on a result of Derdzi\'nski [11], we prove the convexity of complete 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$. More precisely, for $n\geq 3$, we show that any $n$-dimensional complete 2-convex translating solitons are convex, and any $n$-dimensional complete 2-convex self-expanders asymptotic to (strictly) mean convex cones are convex. Comment: 15 pages |
| Databáze: | arXiv |
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