Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

Erwann Delay (1) , Jérémie Fougeirol (1, 2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 IMAG - Institut Montpelliérain Alexander Grothendieck

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 Poincaré and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.

Keywords: Hilbert manifold; asymptotically hyperbolic; elliptic operators; general relativity; constraint equations; weak regularity

Domains: Differential Geometry [math.DG]; General Relativity and Quantum Cosmology [gr-qc]

Erwann Delay, Jérémie Fougeirol. Hilbert manifold structure for asymptotically hyperbolic relativistic initial data. 2016. ⟨hal-01346853v2⟩