A Limit Equation Associated To The Solvability Of The Vacuum Einstein Constraint Equations By Using The Conformal Method
2012 (English)In: Duke mathematical journal, ISSN 0012-7094, Vol. 161, no 14, 2669-2697 p.Article in journal (Refereed) Published
Let (M, g) be a compact Riemannian manifold on which a trace-free and divergence-free sigma is an element of W-1,W-p and a positive function tau is an element of W-1,W-p, p > n are fixed. In this paper, we study the vacuum Einstein constraint equations by using the well-known conformal method with data sigma and tau. We show that if no solution exists, then there is a nontrivial solution of another nonlinear limit equation on 1-forms. This last equation can be shown to be without solutions in many situations. As a corollary, we get the existence of solutions of the vacuum Einstein constraint equation under explicit assumptions which, in particular, hold on a dense set of metrics g for the C-0-topology.
Place, publisher, year, edition, pages
2012. Vol. 161, no 14, 2669-2697 p.
Mean-Curvature Solutions, Rough Solutions, Manifolds
IdentifiersURN: urn:nbn:se:kth:diva-107077DOI: 10.1215/00127094-1813182ISI: 000310825200001ScopusID: 2-s2.0-84871269380OAI: oai:DiVA.org:kth-107077DiVA: diva2:575346
QC 201212102012-12-102012-12-062012-12-10Bibliographically approved