Related papers: Solutions to the Einstein-scalar field constraint …
In this note we prove an existence result for the Einstein conformal constraint equations for metrics with vanishing Yamabe invariant assuming that the TT-tensor is small in $L^2$.
In this short note, we give a construction of solutions to the Einstein constraint equations using the well known conformal method. Our method gives a result similar to the one in [15, 16, 24], namely existence when the so called TT-tensor…
We continue the study of the Einstein constraint equations on compact manifolds with boundary initiated by Holst and Tsogtgerel. In particular, we consider the full system and prove existence of solutions in both the near-CMC and…
We prove the existence of solutions to the conformal Einstein-scalar constraint system of equations for closed compact Riemannian manifolds in the positive case. Our results apply to the vacuum case with positive cosmological constant and…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
In this article, we give nonexistence and nonuniqueness results for the vacuum Einstein conformal constraint equations in the far-from-CMC case and also show that in some cases the equations of the conformal method for positive Yamabe…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have…
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 solutions using a combination of a priori estimates for the…
The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
We extend the study of the vacuum Einstein constraint equations on manifolds with ends of cylindrical type initiated by Chru\'sciel and Mazzeo by finding a class of solutions to the fully coupled system on such manifolds. We show that given…
In this paper we analyse semi-linear systems of partial differential equations which are motivated by the conformal formulation of the Einstein constraint equations coupled with realistic physical fields on asymptotically Euclidean (AE)…
In this article we consider the conformal decomposition of the Einstein constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in…
This article describes some geometric invariants and conformal anomalies for conformally compact Einstein manifolds and their minimal submanifolds which have recently been discovered via the Anti-de Sitter/Conformal Field Theory…
We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D. Pollack in the case of closed manifolds and establish existence and non-existence results for the Einstein-scalar field constraint equations on asymptotically…
We construct low regularity solutions of the vacuum Einstein constraint equations on compact manifolds. On 3-manifolds we obtain solutions with metrics in $H^s$ where $s>3/2$. The constant mean curvature (CMC) conformal method leads to a…
We consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz and York, on a compact manifold with boundary. We use order relations on appropriate Banach spaces to derive weak solution generalizations…
In this article we develop some new existence results for the Einstein constraint equations using the Lichnerowicz-York conformal rescaling method. The mean extrinsic curvature is taken to be an arbitrary smooth function without…
We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field…