Rigidity of area-minimizing two-spheres in three-manifolds

2010/02/15 by H. Bray, Hubert L. Bray, S. Brendle +6 · 11 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1002.2814

Final version, to appear in Comm Anal Geom

openalex publication_date 2010/02/15 · arxiv created 2010/09/28 · arxiv updated 2010/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a sharp upper bound for the area of a minimal two-sphere in a three-manifold (M,g) with positive scalar curvature. If equality holds, we show that the universal cover of (M,g) is isometric to a cylinder.

Citations

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

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