A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold

Details A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold

2010-12-10

arxiv.org/abs/1012.2246v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

remark on the equivalence between the existence of a solution to the Lichnerowicz equation and to the prescribed scalar curvat

Scientific paper

We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain exponent appearing in the equations, constructing solutions of these sub-critical equations and then in letting the exponent tend to its true value. We prove that the solutions of the sub-critical equations remain bounded which yields solutions of the constraint equation unless a certain limit equation admits a non-trivial solution. Finally, we give conditions which ensure that the limit equation admits no non-trivial solution.

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