De l'équation de prescription de courbure scalaire aux équations de contrainte en relativité générale sur une variété asymptotiquement hyperbolique

Two problems concerning asymptotically hyperbolic manifolds with an inner boundary are studied. First, we study scalar curvature presciption with either Dirichlet or mean curvature prescription interior boundary condition. Then we apply those results to the Lichnerowicz equation with (future or past...

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Bibliographic Details
Published in:Journal de mathématiques pures et appliquées 2010-08, Vol.94 (2), p.200-227
Main Author: Gicquaud, Romain
Format: Article
Language:fre
Subjects:
Differential Geometry
General Relativity and Quantum Cosmology
Mathematics
Physics
Online Access:Get full text
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Summary:Two problems concerning asymptotically hyperbolic manifolds with an inner boundary are studied. First, we study scalar curvature presciption with either Dirichlet or mean curvature prescription interior boundary condition. Then we apply those results to the Lichnerowicz equation with (future or past) apparent horizon interior boundary condition. In the last part we show how to construct TT-tensors. Thus we obtain Cauchy data with constant mean curvature for Einstein vacuum equations.
ISSN:0021-7824
DOI:10.1016/j.matpur.2010.03.011