Stable -th capillary hypersurfaces
Jinyu Guo
Fujian Normal University, Fuzhou, P. R. ChinaHaizhong Li
Tsinghua University, Beijing, P. R. ChinaChao Xia
Xiamen University, P. R. China

Abstract
In this paper, we propose a new definition of stable -th capillary hypersurfaces from variational perspective for any . More precisely, we define stable -th capillary hypersurfaces to be smooth local minimizers of a new energy functional under volume-preserving and contact angle-preserving variations. Using this new concept of stable -th capillary hypersurfaces, we generalize the stability results of Souam (2023) in a Euclidean half-space, and Guo, Wang and Xia (2022) in a horoball in hyperbolic space for capillary hypersurfaces to the -th capillary hypersurface case.
Cite this article
Jinyu Guo, Haizhong Li, Chao Xia, Stable -th capillary hypersurfaces. Rev. Mat. Iberoam. 41 (2025), no. 5, pp. 1629–1664
DOI 10.4171/RMI/1558