Perturbative solutions to the extended constant scalar curvature equations on asymptotically hyperbolic manifolds
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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.References
- Michael T. Anderson, Piotr T. Chruściel, and Erwann Delay, Non-trivial, static, geodesically complete space-times with a negative cosmological constant. II. $n\geq 5$, AdS/CFT correspondence: Einstein metrics and their conformal boundaries, IRMA Lect. Math. Theor. Phys., vol. 8, Eur. Math. Soc., Zürich, 2005, pp. 165–204. MR 2160871
- Lars Andersson and Piotr T. Chruściel, Solutions of the constraint equations in general relativity satisfying “hyperboloidal boundary conditions”, Dissertationes Math. (Rozprawy Mat.) 355 (1996), 100. MR 1405962
- Lars Andersson and Vincent Moncrief, Elliptic-hyperbolic systems and the Einstein equations, Ann. Henri Poincaré 4 (2003), no. 1, 1–34. MR 1967177, DOI 10.1007/s00023-003-0120-1
- Adrian Butscher, Exploring the conformal constraint equations, The conformal structure of space-time, Lecture Notes in Phys., vol. 604, Springer, Berlin, 2002, pp. 195–222. MR 2007930, DOI 10.1007/3-540-45818-2_{1}0
- Adrian Butscher, Perturbative solutions of the extended constraint equations in general relativity, Comm. Math. Phys. 272 (2007), no. 1, 1–23. MR 2291799, DOI 10.1007/s00220-007-0204-8
- Piotr T. Chruściel and Helmut Friedrich (eds.), The Einstein equations and the large scale behavior of gravitational fields, Birkhäuser Verlag, Basel, 2004. 50 years of the Cauchy problem in general relativity. MR 2098911, DOI 10.1007/978-3-0348-7953-8
- R. Gicquaud, De l’équation de prescription de courbure scalaire aux équations de contrainte en relativité générale sur une variété asymptotiquement hyperbolique (2008), arXiv:0802.3279.
- C. Robin Graham and John M. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 (1991), no. 2, 186–225. MR 1112625, DOI 10.1016/0001-8708(91)90071-E
- John M. Lee, Fredholm operators and Einstein metrics on conformally compact manifolds, Mem. Amer. Math. Soc. 183 (2006), no. 864, vi+83. MR 2252687, DOI 10.1090/memo/0864
- Rafe Mazzeo, The Hodge cohomology of a conformally compact metric, J. Differential Geom. 28 (1988), no. 2, 309–339. MR 961517
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
- MR Author ID: 630272
- Email: Erwann.Delay@univ-avignon.fr
- Received by editor(s): March 17, 2008
- Published electronically: February 20, 2009
- Communicated by: Matthew J. Gursky
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2293-2298
- MSC (2000): Primary 35J50, 58J05, 35J70, 35J60, 35Q75
- DOI: https://doi.org/10.1090/S0002-9939-09-09703-2
- MathSciNet review: 2495262