Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
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| Format: | Preprint |
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2021
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| _version_ | 1866911452437151744 |
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| author | Weng, Liangjun Xia, Chao |
| author_facet | Weng, Liangjun Xia, Chao |
| contents | In this paper, we first introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball $\mathbb{B}^{n+1}$ and derive its first variational formula. Then by using a locally constrained nonlinear curvature flow, which preserves the $n$-th quermassintegral and non-decreases the $k$-th quermassintegral, we obtain the Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in $\mathbb{B}^{n+1}$. This generalizes the result in \cite{SWX} for convex hypersurfaces with free boundary in $\mathbb{B}^{n+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05773 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball Weng, Liangjun Xia, Chao Differential Geometry Analysis of PDEs 53C21, 53C44, 35K96 In this paper, we first introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball $\mathbb{B}^{n+1}$ and derive its first variational formula. Then by using a locally constrained nonlinear curvature flow, which preserves the $n$-th quermassintegral and non-decreases the $k$-th quermassintegral, we obtain the Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in $\mathbb{B}^{n+1}$. This generalizes the result in \cite{SWX} for convex hypersurfaces with free boundary in $\mathbb{B}^{n+1}$. |
| title | Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball |
| topic | Differential Geometry Analysis of PDEs 53C21, 53C44, 35K96 |
| url | https://arxiv.org/abs/2111.05773 |