Uniqueness of the foliation of constant mean curvature spheres in asymptotically flat 3-manifolds

Shiguang Ma

Vol. 252 (2011), No. 1, 145–179

DOI: 10.2140/pjm.2011.252.145

Abstract

This paper studies the constant mean curvature surface in asymptotically flat 3-manifolds with general asymptotics. Under some weak conditions, the foliation of stable spheres of constant mean curvature is shown to be unique outside some compact set in the asymptotically flat 3-manifold with positive mass.

Keywords

constant mean curvature, foliation, asympotically flat manifold

Mathematical Subject Classification 2000

Primary: 53C20

Secondary: 58E20, 83C99

Milestones

Received: 19 August 2010

Accepted: 7 December 2010

Published: 8 October 2011

Proposed: Jie Qing