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

Abstract

The purpose of this article is study rigidity of free boundary minimal two-disk that locally maximize the modified Hawking mass on a Riemannian three-manifold with positive lower bound on its scalar curvature and mean convex boundary. Under strict stability of it assumptions, we prove that a neighborhood of it in M is isometric to one of the half de Sitter-Schwarzschild metrics.Comment: 16 pages; no figure