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

André Neves; Gang Tian

doi:10.1515/CRELLE.2010.028

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

André Neves, Gang Tian

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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 Mller.

Original language	English (US)
Pages (from-to)	69-93
Number of pages	25
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	641
DOIs	https://doi.org/10.1515/CRELLE.2010.028
State	Published - Apr 2010

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/CRELLE.2010.028

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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 Mller.",

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AB - 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 Mller.

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

Abstract

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