Hausdorff dimension and limits of Kleinian groups

In this paper we prove that if M is a compact, hyperbolizable 3-manifold, w hich is not a handlebody, then the Hausdorff dimension of the limit set is continuous in the strong topology on the space of marked hyperbolic 3-manif olds homotopy equivalent to M. We similarly observe that for any compact hy perbolizable 3-manifold M (including a handlebody), the bottom of the spect rum of the Laplacian gives a continuous function in the strong topology on the space of topologically tame hyperbolic 3-manifolds homotopy equivalent to M.