Erwann Delay (Avignon)
We will see that the Corvino gluing technique can be adapted to the asymptotically hyperbolic context. More precisely, if a Riemannian metric with constant negative scalar curvature is asymptotic to a hyperbolic model at infinity, it can be glued on an "annulus" with a Schwarzschild-AdS slice to a new constant scalar curvature metric. This produce initial data for the vacuum Einstein equation that are exactly Schwarzschild-AdS slice outside of a compact set. This is joint work with Piotr Chrusciel.