Area-minimizing surfaces in asymptotically flat three-manifolds

2015/10/26 by Otis Chodosh, Chodosh, Otis, Michael Eichmair +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1510.07406

openalex publication_date 2015/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that an asymptotically flat Riemannian three-manifold with non-negative scalar curvature is isometric to flat ℝ³ if it admits an unbounded area-minimizing surface. This answers a question of R. Schoen.

Citations

• On the proof of the positive mass conjecture in general relativity

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