Capillary hypersurfaces, Heintze-Karcher's inequality and Zermelo's navigation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910298757136384 |
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| author | Wang, Guofang Xia, Chao |
| author_facet | Wang, Guofang Xia, Chao |
| contents | In this paper, we establish a Heintze-Karcher-type inequality for capillary hypersurfaces in a unit ball. To achieve this, we introduce a special Finsler metric given by Zermelo's navigation and study the geodesic normal flow with respect to this Finsler metric. Our results indicate that the relationship between capillary hypersufaces and hypersurfaces with free boundary is similar to the one between Finsler geometry and Riemannian geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Capillary hypersurfaces, Heintze-Karcher's inequality and Zermelo's navigation Wang, Guofang Xia, Chao Differential Geometry In this paper, we establish a Heintze-Karcher-type inequality for capillary hypersurfaces in a unit ball. To achieve this, we introduce a special Finsler metric given by Zermelo's navigation and study the geodesic normal flow with respect to this Finsler metric. Our results indicate that the relationship between capillary hypersufaces and hypersurfaces with free boundary is similar to the one between Finsler geometry and Riemannian geometry. |
| title | Capillary hypersurfaces, Heintze-Karcher's inequality and Zermelo's navigation |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2401.08450 |