Mapping properties of the Laplacian in Sobolev spaces of forms on complete hyperbolic manifolds

For a complete manifold M with constant negative curvature, we prove that the rough Laplacian Delta(R) defines topological isomorphisms in the scale of Sobolev spaces H-p(s)(M) of p-forms for all p, 0 < p < n. For the de Rham Laplacian Delta and M = H-n, the Poincare hyperbolic space, this is shown too for 0 less than or equal to p less than or equal to n, p not equal n/2, p not equal (n +/- 1)/2.