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

2007/11/27 by André Neves, Andre Neves, Gang Tian +2
Mathematics · #53A10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.AP #math.DG #msc:53A10

paper · pdf · doi:10.48550/arxiv.0711.4331

24 pages, submitted

arxiv created 2007/11/27 · openalex publication_date 2007/11/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a previous paper, the authors showed that metrics which are asymptotic to Anti-de Sitter-Schwarzschild metrics with positive mass admit a unique foliation by stable spheres with constant mean curvature. In this paper we extend that result to all asymptotically hyperbolic metrics for which the trace of the mass term is positive. We do this by combining the Kazdan-Warner obstructions with a theorem due to De Lellis and Müller.

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