Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds

Otis Chodosh; Michael Eichmair; Yuguang Shi; Haobin Yu

doi:10.1002/cpa.21981

Titel

Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds

Autor*in

Otis Chodosh

Department of Mathematics, Stanford University

Michael Eichmair

Fakultät für Mathematik, Universität Wien

Yuguang Shi

Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University

... show all

Abstract

Let (M, g) be an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and positive mass. We show that each leaf of the canonical foliation of the end of (M, g) through stable constant mean curvature spheres encloses more volume than any other surface of the same area. Unlike all previous characterizations of large solutions of the isoperimetric problem, we need no asymptotic symmetry assumptions beyond the optimal conditions for the positive mass theorem. This generality includes examples where global uniqueness of the leaves of the canonical foliation as stable constant mean curvature spheres fails dramatically. Our results here resolve a question of G. Huisken on the isoperimetric content of the positive mass theorem.

Stichwort

Applied MathematicsGeneral Mathematics

Objekt-Typ

journal article

Sprache

Englisch [eng]

Persistent identifier

https://phaidra.univie.ac.at/o:1437493

DOI

10.1002/cpa.21981

Erschienen in

Titel