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

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

2007-11-27

arxiv.org/abs/0711.4331v1

Mathematics

Differential Geometry

24 pages, submitted

Scientific paper

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 M\"uller.

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