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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00783626
Contributor : Romain Gicquaud <>
Submitted on : Friday, February 1, 2013 - 1:33:37 PM
Last modification on : Thursday, March 5, 2020 - 5:33:44 PM

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Romain Gicquaud, Anna Sakovich. A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold. Communications in Mathematical Physics, Springer Verlag, 2012, 310 (3), pp.705-763. ⟨10.1007/s00220-012-1420-4⟩. ⟨hal-00783626⟩

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