Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929337290194944 |
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| author | Jia, Xiaohan Wang, Guofang Xia, Chao Zhang, Xuwen |
| author_facet | Jia, Xiaohan Wang, Guofang Xia, Chao Zhang, Xuwen |
| contents | In this paper, we show that any embedded capillary hypersurface in the half-space with anisotropic constant mean curvature is a truncated Wulff shape. This extends Wente's result \cite{Wente80} to the anisotropic case and He-Li-Ma-Ge's result \cite{HLMG09} to the capillary boundary case. The main ingredients in the proof are a new Heintze-Karcher inequality and a new Minkowski formula, which have their own inetrest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_02913 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space Jia, Xiaohan Wang, Guofang Xia, Chao Zhang, Xuwen Differential Geometry 53C24, 35J25, 53C21 In this paper, we show that any embedded capillary hypersurface in the half-space with anisotropic constant mean curvature is a truncated Wulff shape. This extends Wente's result \cite{Wente80} to the anisotropic case and He-Li-Ma-Ge's result \cite{HLMG09} to the capillary boundary case. The main ingredients in the proof are a new Heintze-Karcher inequality and a new Minkowski formula, which have their own inetrest. |
| title | Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space |
| topic | Differential Geometry 53C24, 35J25, 53C21 |
| url | https://arxiv.org/abs/2211.02913 |