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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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Neves, A., Tian, G. Existence and Uniqueness of Constant Mean Curvature Foliation of Asymptotically Hyperbolic 3-Manifolds. Geom. Funct. Anal. 19, 910–942 (2009). https://doi.org/10.1007/s00039-009-0019-1
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DOI: https://doi.org/10.1007/s00039-009-0019-1