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Perturbative solutions to the extended constant scalar curvature equations on asymptotically hyperbolic manifolds

Author: Erwann Delay
Journal: Proc. Amer. Math. Soc. 137 (2009), 2293-2298
MSC (2000): Primary 35J50, 58J05, 35J70, 35J60, 35Q75
Published electronically: February 20, 2009
MathSciNet review: 2495262
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Abstract: The extended constant scalar curvature equations is a particular case of the conformal contraint equations introduced by H. Friedrich. It was first studied by A. Butscher in an asymptotically flat setting. We prove the local existence of solutions to the extended constant scalar curvature equations near some asymptotically hyperbolic Einstein metrics. This gives a new local construction of asymptotically hyperbolic metrics with constant scalar curvature.

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Additional Information

Erwann Delay
Affiliation: Institut de Mathématiques et Modélisation de Montpellier, UMR 5149 CNRS, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier cedex 5, France
Address at time of publication: Laboratoire d’Analyse Non linéaire et Géométrie (EA2151), Faculté des Sciences, 33 rue Louis Pasteur, F-84000 Avignon, France

Keywords: Asymptotically hyperbolic manifolds, general relativity, constraint equations, symmetric 2-tensor, asymptotic behavior
Received by editor(s): March 17, 2008
Published electronically: February 20, 2009
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2009 American Mathematical Society

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