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arXiv · 2311.11333

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

Jinyu Guo·Haizhong Li·Chao Xia
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Abstract

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.

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Jinyu Guo, Haizhong Li, Chao Xia. 2023-11-19. Stable $(r+1)$-th capillary hypersurfaces. https://doi.org/10.4171/rmi%2F1558

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