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

2005/06/01 by Jie Qing, Gang Tian, Qing, Jie +1 · 1 citation
Mathematics · Physics and Astronomy · #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53C43 #msc:58E20

paper · pdf · doi:10.48550/arxiv.math/0506005

22 pages

arxiv created 2005/08/11 · arxiv updated 2009/12/01

Abstract

In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature outside a fixed compact subset are unique. Therefore we are able to conclude that there is a unique foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass.

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• Constant Harmonic Mean Curvature Foliation in Asymptotic Schwarzschild Spaces-II

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