The Einstein-scalar field constraint system in the positive case

Abstract

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 to the massive Klein-Gordon setting.

14 pages

References in corpus (3)

• Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics
• 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 (3)

• The Constraint Equations in the Presence of a Scalar Field - the Case of the Conformal Method with Volumetric Drift
• Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary
• Einstein-type elliptic systems