Anisotropic capillary hypersurfaces in a wedge
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909442702835712 |
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| author | Ma, Hui Ma, Jiaxu Yang, Mingxuan |
| author_facet | Ma, Hui Ma, Jiaxu Yang, Mingxuan |
| contents | We investigate anisotropic capillary hypersurfaces within a wedge in Euclidean space. In this study, we generalize the Minkowski norm \(F\), traditionally employed to define the anisotropic surface energy, to a gauge on the unit sphere \(S^n\). This generalization helps to illuminate a significant relationship between capillary hypersurfaces and hypersurfaces with free boundary. Our main results include new Minkowski formulae and a Heintze-Karcher type inequality. As an application, we prove an Alexandrov-type theorem, thereby extending the known results to the anisotropic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19815 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anisotropic capillary hypersurfaces in a wedge Ma, Hui Ma, Jiaxu Yang, Mingxuan Differential Geometry 53C24, 53C42, 53C40 We investigate anisotropic capillary hypersurfaces within a wedge in Euclidean space. In this study, we generalize the Minkowski norm \(F\), traditionally employed to define the anisotropic surface energy, to a gauge on the unit sphere \(S^n\). This generalization helps to illuminate a significant relationship between capillary hypersurfaces and hypersurfaces with free boundary. Our main results include new Minkowski formulae and a Heintze-Karcher type inequality. As an application, we prove an Alexandrov-type theorem, thereby extending the known results to the anisotropic setting. |
| title | Anisotropic capillary hypersurfaces in a wedge |
| topic | Differential Geometry 53C24, 53C42, 53C40 |
| url | https://arxiv.org/abs/2403.19815 |