Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

Abstract

We provide a Hilbert manifold structure {à} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{é} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.

References in corpus (5)

• On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications
• Overview of the proof of the Bounded $L^2$ Curvature Conjecture
• The mass of asymptotically hyperbolic Riemannian manifolds
• Asymptotically hyperbolic manifolds with small mass
• Hilbert Manifold Structure of The Set of Solutions of Constraint Equations For Coupled Einstein and Scalar Fields