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

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

2006-10-25

arxiv.org/abs/math/0610767v2

Mathematics

Differential Geometry

39 pages, submitted. Decay conditions on Lemma 6.3 and Theorem 1.3 corrected

Scientific paper

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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