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- Title
A Large Class of Non-Constant Mean Curvature Solutions of the Einstein Constraint Equations on an Asymptotically Hyperbolic Manifold.
- Authors
Gicquaud, Romain; Sakovich, Anna
- 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.
- Subjects
NUMERICAL solutions to Einstein field equations; CURVATURE; CONSTRAINTS (Physics); ASYMPTOTIC expansions; HYPERBOLIC differential equations; MANIFOLDS (Mathematics); CRITICAL point theory; EXPONENTS
- Publication
Communications in Mathematical Physics, 2012, Vol 310, Issue 3, p705
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-012-1420-4