English

Stable anisotropic capillary hypersurfaces in a half-space

Differential Geometry 2024-03-15 v2

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.

Keywords

Cite

@article{arxiv.2301.03020,
  title  = {Stable anisotropic capillary hypersurfaces in a half-space},
  author = {Jinyu Guo and Chao Xia},
  journal= {arXiv preprint arXiv:2301.03020},
  year   = {2024}
}

Comments

20 pages,final version,to appear in Indiana U. Math. J

R2 v1 2026-06-28T08:06:37.055Z