Generalized Minkowski formulas and rigidity results for anisotropic capillary hypersurfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912380229779456 |
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| author | Gao, Jinyu Li, Guanghan |
| author_facet | Gao, Jinyu Li, Guanghan |
| contents | In this paper, we obtain a new Hsiung-Minkowski integral formula for anisotropic capillary hypersurfaces in the half-space, which includes the weighted Hsiung-Minkowski formula and classical anisotropic Minkowski identity for closed hypersurfaces as special cases. As applications, we prove some anisotropic Alexandrov-type theorems and rigidity results for anisotropic capillary hypersurfaces. Specially, the uniqueness of the solution to the anisotropic Orlicz-Christoffel-Minkowski problem is obtained, and thus a new proof is provided for the uniqueness of the solution to $L_p$-Minkowski problem with $p\geq 1$ in the Euclidean capillary convex bodies geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Minkowski formulas and rigidity results for anisotropic capillary hypersurfaces Gao, Jinyu Li, Guanghan Differential Geometry 53A10, 53C24, 53C40 In this paper, we obtain a new Hsiung-Minkowski integral formula for anisotropic capillary hypersurfaces in the half-space, which includes the weighted Hsiung-Minkowski formula and classical anisotropic Minkowski identity for closed hypersurfaces as special cases. As applications, we prove some anisotropic Alexandrov-type theorems and rigidity results for anisotropic capillary hypersurfaces. Specially, the uniqueness of the solution to the anisotropic Orlicz-Christoffel-Minkowski problem is obtained, and thus a new proof is provided for the uniqueness of the solution to $L_p$-Minkowski problem with $p\geq 1$ in the Euclidean capillary convex bodies geometry. |
| title | Generalized Minkowski formulas and rigidity results for anisotropic capillary hypersurfaces |
| topic | Differential Geometry 53A10, 53C24, 53C40 |
| url | https://arxiv.org/abs/2401.12137 |