Hilbert manifold structure for asymptotically hyperbolic relativistic   initial data
  We provide a Hilbert manifold structure {\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric. 
Erwann Delay (LMA), J\'er\'emie Fougeirol (LMA, IMAG)
math.DG gr-qc