Translator Disclaimer
1 November 2012 A limit equation associated to the solvability of the vacuum Einstein constraint equations by using the conformal method
Mattias Dahl, Romain Gicquaud, Emmanuel Humbert
Duke Math. J. 161(14): 2669-2697 (1 November 2012). DOI: 10.1215/00127094-1813182

Abstract

Let (M,g) be a compact Riemannian manifold on which a trace-free and divergence-free σW1,p and a positive function τW1,p, p>n are fixed. In this paper, we study the vacuum Einstein constraint equations by using the well-known conformal method with data σ and τ. 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 C0-topology.

Citation

Download Citation

Mattias Dahl. Romain Gicquaud. Emmanuel Humbert. "A limit equation associated to the solvability of the vacuum Einstein constraint equations by using the conformal method." Duke Math. J. 161 (14) 2669 - 2697, 1 November 2012. https://doi.org/10.1215/00127094-1813182

Information

Published: 1 November 2012
First available in Project Euclid: 26 October 2012

zbMATH: 1258.53037
MathSciNet: MR2993137
Digital Object Identifier: 10.1215/00127094-1813182

Subjects:
Primary: 53C21
Secondary: 35Q75, 53C80, 83C05

Rights: Copyright © 2012 Duke University Press

JOURNAL ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.161 • No. 14 • 1 November 2012
Back to Top