Stable anisotropic capillary hypersurfaces in a half-space

Jinyu Guo; Chao Xia

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arXiv · 2301.03020

Stable anisotropic capillary hypersurfaces in a half-space

Jinyu Guo·Chao Xia

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Abstract

In this paper, we study stability problem of anisotropic capillary hypersurfaces in an Euclidean half-space. We prove that any compact immersed anisotropic capillary constant anisotropic mean curvature hypersurface in the half-space is weakly stable if and only if it is a truncated Wulff shape. On the other hand, we prove a Bernstein-type theorem for stable anisotropic capillary minimal surfaces in the three dimensional half-space under Euclidean area growth assumption.

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Jinyu Guo, Chao Xia. 2023-01-08. Stable anisotropic capillary hypersurfaces in a half-space. https://arxiv.org/abs/2301.03020

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