The Exponent of Convergence of Kleinian Groups; on a Theorem of Bishop and Jones

B O Stratmann

In this note we give a characterization of the Hausdorff dimensional significance of the exponent of convergence for any arbitrary Kleinian group. We show that this exponent is always equal to the Hausdorff dimension of the uniformly radial limit sets of the Kleinian group. We give a detailed and elementary proof of this important fact, clarifying and generalizing a result of Bishop and Jones.