Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916927910182912 |
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| author | Xie, Junming |
| author_facet | Xie, Junming |
| contents | In this paper, we investigate the convexity of mean convex asymptotically conical self-expanders to the mean curvature flow in $\mathbb{R}^{n+1}$. Specifically, for $n\geq 3$, we show that any $n$-dimensional complete mean convex self-expander asymptotic to mean convex and weakly convex cones must be strictly convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01023 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow Xie, Junming Differential Geometry 53E10, 53C21, 53C42 In this paper, we investigate the convexity of mean convex asymptotically conical self-expanders to the mean curvature flow in $\mathbb{R}^{n+1}$. Specifically, for $n\geq 3$, we show that any $n$-dimensional complete mean convex self-expander asymptotic to mean convex and weakly convex cones must be strictly convex. |
| title | Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow |
| topic | Differential Geometry 53E10, 53C21, 53C42 |
| url | https://arxiv.org/abs/2509.01023 |