2021/11/02 by Rabah Souam, Souam, Rabah · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2111.01500
openalex publication_date 2021/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study stable immersed capillary hypersurfaces Σ in domains B of R n+1 bounded by hyperplanes. When B is a half-space, we show Σ is a spherical cap. When B is a domain bounded by k hyperplanes P 1 ,. .. , P k , 2 ≤ k ≤ n + 1, having independent normals, and Σ has contact angle θ i with P i and does not touch the vertices of B, we prove there exists δ > 0, depending only on P 1 ,. .. , P k , so that if θ i ∈ (π 2 -- δ, π 2 + δ) for each i, then Σ has to be a piece of a sphere.