A Large Class of Non-Constant Mean Curvature Solutions of the Einstein Constraint Equations on an Asymptotically Hyperbolic Manifold
2012 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 310, no 3, 705-763 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2012. Vol. 310, no 3, 705-763 p.
IdentifiersURN: urn:nbn:se:kth:diva-27202DOI: 10.1007/s00220-012-1420-4ISI: 000301492300006OAI: oai:DiVA.org:kth-27202DiVA: diva2:375756
QC 201204112010-12-092010-12-092012-09-28Bibliographically approved