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

André Neves; Gang Tian

doi:10.1007/s00039-009-0019-1

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

André Neves, Gang Tian

Mathematics

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

16 Scopus citations

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.

Original language	English (US)
Pages (from-to)	910-942
Number of pages	33
Journal	Geometric and Functional Analysis
Volume	19
Issue number	3
DOIs	https://doi.org/10.1007/s00039-009-0019-1
State	Published - 2009

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Keywords

Constant mean curvature
Foliations

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10.1007/s00039-009-0019-1

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title = "Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds",

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.",

keywords = "Constant mean curvature, Foliations",

author = "Andr{\'e} Neves and Gang Tian",

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AU - Neves, André

AU - Tian, Gang

PY - 2009

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N2 - 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.

AB - 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.

KW - Constant mean curvature

KW - Foliations

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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