Uniqueness of the Foliation of Constant Mean Curvature Spheres in Asymptotically Flat 3-Manifolds

TL;DR

This paper proves the uniqueness of foliations by stable constant mean curvature spheres in asymptotically flat 3-manifolds with positive mass under weak conditions, extending understanding of geometric structures at infinity.

Contribution

It establishes the uniqueness of constant mean curvature sphere foliations in a broad class of asymptotically flat 3-manifolds, generalizing previous results.

Findings

Uniqueness of stable CMC sphere foliation outside a compact set

Applicability to manifolds with weak asymptotic conditions

Extension of geometric analysis in general relativity contexts

Abstract

In this paper I study the constant mean curvature surface in asymptotically flat 3-manifolds with general asymptotics. Under some weak condition, I prove that outside some compact set in the asymptotically flat 3-manifold with positive mass, the foliation of stable spheres of constant mean curvature is unique.