Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds

Abstract

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 hyperbolic manifolds.

15 pages

References in corpus (2)

• A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
• The constraint equations for the Einstein-scalar field system on compact manifolds

Cited by in corpus (4)

• A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold
• Asymptotic behavior of a matter filled universe with exotic topology
• Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation
• Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS