We present the state-of-the-art concerning the relativistic constraints, which describe the
geometry of hypersurfaces in a spacetime subject to the Einstein field equations. We review …

This book offers a systematic exposition of conformal methods and how they can be used to
study the global properties of solutions to the equations of Einstein's theory of gravity. It …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

We consider the conformal decomposition of Einstein's constraint equations introduced by
Lichnerowicz and York, on a closed manifold. We establish existence of non-CMC weak …

Let (M, g) be a compact Riemannian manifold on which a trace-free and divergence-free σ∈
W 1, p and a positive function τ∈ W 1, p, p> n are fixed. In this paper, we study the vacuum …

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 …

We survey some results on scalar curvature and properties of solutions to the Einstein
constraint equations. Topics include an extended discussion of asymptotically flat solutions …

While there exist now formulations of initial boundary value problems for Einstein's field
equations which are well posed and preserve constraints and gauge conditions, the …

In this paper, we give a construction of the solutions to the Einstein constraint equations
using the well-known conformal method. Our method gives a result similar to the one in [14 …

arXiv:1201.4937v2 [gr-qc] 7 Oct 2014 Page 1 UWThPh-2011-43 Initial data sets with ends of
cylindrical type: I. The Lichnerowicz equation Piotr T. Chrusciel∗ IHES, Bures-sur-Yvette, and …