Stable $(r+1)$-th capillary hypersurfaces

Fuente: arXiv
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Main Authors: Guo, Jinyu, Li, Haizhong, Xia, Chao
Format: Preprint
Published: 2023
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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
id 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