Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908838238617600 |
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| author | Wang, Guofang Weng, Liangjun Xia, Chao |
| author_facet | Wang, Guofang Weng, Liangjun Xia, Chao |
| contents | In this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-space. Then we solve the related isoperimetric type problems for the convex capillary hypersurfaces and obtain the corresponding Alexandrov-Fenchel inequalities. In order to prove these results, we construct a new locally constrained curvature flow and prove that the flow converges globally to a spherical cap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_04639 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary Wang, Guofang Weng, Liangjun Xia, Chao Differential Geometry Analysis of PDEs In this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-space. Then we solve the related isoperimetric type problems for the convex capillary hypersurfaces and obtain the corresponding Alexandrov-Fenchel inequalities. In order to prove these results, we construct a new locally constrained curvature flow and prove that the flow converges globally to a spherical cap. |
| title | Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2206.04639 |