2023/11/19 by Jinyu Guo, Haizhong Li, Guo, Jinyu +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2311.11333
openalex publication_date 2023/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
In this paper, we propose a new definition of stable (r+1)-th capillary hypersurfaces from variational perspective for any 1≤ r≤ 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 \citeSouam in a Euclidean half-space and Guo-Wang-Xia \citeGWX in a horoball in hyperbolic space for capillary hypersurface to (r+1)-th capillary hypersurface case.