Heintze-Karcher inequality and capillary hypersurfaces in a wedge
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912891792261120 |
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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 utilize the method of Heintze-Karcher to prove a "best" version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge.
One of new crucial ingredients in the proof is modified parallel hypersurfaces which are very natural to be used to study capillary hypersurfaces. A more technical part is a subtle analysis along the edge of a wedge. As an application, we classify completely embedded capillary constant mean curvature hypersurfaces that hit the edge in a wedge, which is a subtler case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13839 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Heintze-Karcher inequality and capillary hypersurfaces in a wedge Jia, Xiaohan Wang, Guofang Xia, Chao Zhang, Xuwen Differential Geometry 53C24, 35J25, 53C21 In this paper, we utilize the method of Heintze-Karcher to prove a "best" version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge. One of new crucial ingredients in the proof is modified parallel hypersurfaces which are very natural to be used to study capillary hypersurfaces. A more technical part is a subtle analysis along the edge of a wedge. As an application, we classify completely embedded capillary constant mean curvature hypersurfaces that hit the edge in a wedge, which is a subtler case. |
| title | Heintze-Karcher inequality and capillary hypersurfaces in a wedge |
| topic | Differential Geometry 53C24, 35J25, 53C21 |
| url | https://arxiv.org/abs/2209.13839 |