Existence and Uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds

2006/10/25 by André Neves, Gang Tian, Neves, André +1 · 1 citation
Mathematics · Physics and Astronomy · #53A10 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.math/0610767

openalex publication_date 2006/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove existence and uniqueness of foliations by stable spheres with constant mean curvature for 3-manifolds which are asymptotic to Anti-de Sitter-Schwarzschild metrics with positive mass. These metrics arise naturally as spacelike timeslices for solutions of the Einstein equation with a negative cosmological constant.

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