Stable anisotropic capillary hypersurfaces in a half-space
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913264217096192 |
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| author | Guo, Jinyu Xia, Chao |
| author_facet | Guo, Jinyu Xia, Chao |
| contents | In this paper, we study stability problem of anisotropic capillary hypersurfaces in an Euclidean half-space. We prove that any compact immersed anisotropic capillary constant anisotropic mean curvature hypersurface in the half-space is weakly stable if and only if it is a truncated Wulff shape. On the other hand, we prove a Bernstein-type theorem for stable anisotropic capillary minimal surfaces in the three dimensional half-space under Euclidean area growth assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03020 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable anisotropic capillary hypersurfaces in a half-space Guo, Jinyu Xia, Chao Differential Geometry In this paper, we study stability problem of anisotropic capillary hypersurfaces in an Euclidean half-space. We prove that any compact immersed anisotropic capillary constant anisotropic mean curvature hypersurface in the half-space is weakly stable if and only if it is a truncated Wulff shape. On the other hand, we prove a Bernstein-type theorem for stable anisotropic capillary minimal surfaces in the three dimensional half-space under Euclidean area growth assumption. |
| title | Stable anisotropic capillary hypersurfaces in a half-space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2301.03020 |