Effective versions of the positive mass theorem

• 成果类型: Article
• 署名作者: Carlotto, Alessandro; Chodosh, Otis; Eichmair, Michael
• 署名单位: University of Cambridge; University of Vienna
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0667-3
• 发表日期: 2016
• 页码: 975-1016
• 关键词: constant mean-curvature; minimal-surfaces; scalar curvature; isoperimetric regions; 3-manifolds; RIGIDITY; spheres; MANIFOLDS; uniqueness; EXISTENCE

摘要

The study of stable minimal surfaces in Riemannian 3-manifolds (M, g) with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when (M, g) is asymptotically flat and has horizon boundary. As a consequence, we obtain an effective version of the positive mass theorem in terms of isoperimetric or, more generally, closed volume-preserving stable CMC surfaces that is appealing from both a physical and a purely geometric point of view. We also include a proof of the following conjecture of Schoen: An asymptotically flat Riemannian 3-manifold with non-negative scalar curvature that contains an unbounded area-minimizing surface is isometric to flat .