Stable free boundary surfaces with constant extrinsic curvature in 3-dimensional space forms

2023/05/01 by Leonardo M. Damasceno, Damasceno, Leonardo, Maria Fernanda Elbert +1
Mathematics · #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2305.01093

openalex publication_date 2023/05/01 · openalex created_date 2023/05/04 · openalex updated_date 2026/07/28

Abstract

In this paper we use the notion of stability for free boundary surfaces with constant higher order mean curvature to obtain rigidity results for H₂-surfaces with free boundary of a geodesic ball of a simply connected 3-dimensional space form or a slab of ℝ³.

Related

• Free boundary constant mean curvature surfaces in a strictly convex three-manifold
• On stable constant mean curvature surfaces in S2 X R and H2 X R
• Stability and rigidity of extremal surfaces in Riemannian geometry and General Relativity
• The rigidity of embedded constant mean curvature surfaces
• On stable constant mean curvature surfaces with free boundary