References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

A Limit Equation Associated To The Solvability Of The Vacuum Einstein Constraint Equations By Using The Conformal MethodPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2012 (English)In: Duke mathematical journal, ISSN 0012-7094, Vol. 161, no 14, 2669-2697 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2012. Vol. 161, no 14, 2669-2697 p.
##### Keyword [en]

Mean-Curvature Solutions, Rough Solutions, Manifolds
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-107077DOI: 10.1215/00127094-1813182ISI: 000310825200001ScopusID: 2-s2.0-84871269380OAI: oai:DiVA.org:kth-107077DiVA: diva2:575346
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
##### Note

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.

QC 20121210

Available from: 2012-12-10 Created: 2012-12-06 Last updated: 2012-12-10Bibliographically approvedReferences$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1080",{id:"formSmash:lower:j_idt1080",widgetVar:"widget_formSmash_lower_j_idt1080",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1081_j_idt1083",{id:"formSmash:lower:j_idt1081:j_idt1083",widgetVar:"widget_formSmash_lower_j_idt1081_j_idt1083",target:"formSmash:lower:j_idt1081:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});