Effective versions of the positive mass theorem

Alessandro Carlotto, Otis Chodosh, Michael Eichmair

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

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 R3.

Original languageEnglish (US)
Pages (from-to)975-1016
Number of pages42
JournalInventiones Mathematicae
Volume206
Issue number3
DOIs
StatePublished - Dec 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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