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The Hausdorff dimension of the limit set of a geometrically finite Kleinian group

The Hausdorff dimension of the limit set of a geometrically finite Kleinian group

We consider in this paper groups of MObius transformations of l~=RtJ {zc}. Such a group is called Kleinian if it acts discontinuously somewhere in 1~. The action of G extends to the (n+ D-dimensional hyperbolic space H-I=R• zc) and G is geometrically finite if there is a hyperbolic fundamental polyhedron …