Free boundary constant mean curvature surfaces in a strictly convex three-manifold

2021/07/14 by Sung-Hong Min, Min, Sung-Hong, Keomkyo Seo +1
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2107.06458

openalex publication_date 2021/07/14 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

Let C be a strictly convex domain in a 3-dimensional Riemannian manifold with sectional curvature bounded above by a constant and let Σ be a constant mean curvature surface with free boundary in C. We provide a pinching condition on the length of the traceless second fundamental form on Σ which guarantees that the surface is homeomorphic to either a disk or an annulus. Furthermore, under the same pinching condition, we prove that if C is a geodesic ball of 3-dimensional space forms, then Σ is either a spherical cap or a Delaunay surface.

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