Rigidity of free boundary minimal disks in mean convex three-manifolds

2023/09/04 by R. Batista, Batista, Rondinelle, Barnabé Pessoa Lima +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2309.01333

openalex publication_date 2023/09/04 · openalex created_date 2023/09/08 · openalex updated_date 2026/07/28

Abstract

The purpose of this article is study rigidity of free boundary minimal two-disks that locally maximize the modified Hawking mass on a Riemannian three-manifold with positive lower bound on its scalar curvature and mean convex boundary. Assuming the strict stability of Σ, we prove that a neighborhood of it in M is isometric to one of the half de Sitter-Schwarzschild space.

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• Modified Hawking mass and rigidity of three-manifolds with boundary

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