Limit sets of discrete groups of isometries of exotic hyperbolic spaces

Let be a geometrically finite discrete group of isometries of hyperbolic space , where or (in which case ). We prove that the critical exponent of equals the Hausdorff dimension of the limit sets and that the smallest eigenvalue of the Laplacian acting on square integrable functions is a quadratic function of either of them (when they are sufficiently large). A generalization of Hopf ergodicity theorem for the geodesic flow with respect to the Bowen-Margulis measure is also proven.