Stable $(r+1)$-th capillary hypersurfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909888297304064 |
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| author | Guo, Jinyu Li, Haizhong Xia, Chao |
| author_facet | Guo, Jinyu Li, Haizhong Xia, Chao |
| contents | In this paper, we propose a new definition of stable $(r+1)$-th capillary hypersurfaces from variational perspective for any $1\leq r\leq n-1$. More precisely, we define stable $(r+1)$-th capillary hypersurfaces to be smooth local minimizers of a new energy functional under volume-preserving and contact angle-preserving variations. Using the new concept of the stable $(r+1)$-th capillary hypersurfaces, we generalize the stability results of Souam \cite{Souam} in a Euclidean half-space and Guo-Wang-Xia \cite{GWX} in a horoball in hyperbolic space for capillary hypersurface to $(r+1)$-th capillary hypersurface case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_11333 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable $(r+1)$-th capillary hypersurfaces Guo, Jinyu Li, Haizhong Xia, Chao Differential Geometry Analysis of PDEs In this paper, we propose a new definition of stable $(r+1)$-th capillary hypersurfaces from variational perspective for any $1\leq r\leq n-1$. More precisely, we define stable $(r+1)$-th capillary hypersurfaces to be smooth local minimizers of a new energy functional under volume-preserving and contact angle-preserving variations. Using the new concept of the stable $(r+1)$-th capillary hypersurfaces, we generalize the stability results of Souam \cite{Souam} in a Euclidean half-space and Guo-Wang-Xia \cite{GWX} in a horoball in hyperbolic space for capillary hypersurface to $(r+1)$-th capillary hypersurface case. |
| title | Stable $(r+1)$-th capillary hypersurfaces |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2311.11333 |