Convexity of 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916184508596224 |
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| author | Xie, Junming Yu, Jiangtao |
| author_facet | Xie, Junming Yu, Jiangtao |
| contents | In this paper, inspired by the work of Spruck-Xiao [27] and based partly on a result of Derdziński [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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_14281 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convexity of 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$ Xie, Junming Yu, Jiangtao Differential Geometry 53E10, 53C21, 53C42 In this paper, inspired by the work of Spruck-Xiao [27] and based partly on a result of Derdziński [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. |
| title | Convexity of 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$ |
| topic | Differential Geometry 53E10, 53C21, 53C42 |
| url | https://arxiv.org/abs/2211.14281 |