Mass and invariants at infinity for asymptotically hyperbolic manifolds

Some existing results, known as "positive mass theorems", relate global properties of an open smooth manifold with a curvature
condition on a Riemannian metric. For such results, the metric is assumed to be suitably close to a reference geometry at infinity.
This allows existence of "asymptotic invariants" such as the "mass".
In this talk, we will consider more precisely manifolds whose geometry approaches that of the hyperbolic space near infinity.
We will discuss a method for finding all the asymptotic invariants in this case, based on the representation theory for the
group of isometries of the hyperbolic space. This is a work in progress with M. Dahl and R. Gicquaud