Geometric exponents and Kleinian groups

Suppose is the limit set of an analytically finite Kleinian group and that is an enumeration of the components of . Then This had been conjectured by Maskit. We also define a number of different geometric critical exponents associated to a compact set in the plane which generalize the index of Besicovitch and Taylor on the line. Although these exponents may differ for general sets, we show that they are all equal when is the limit set of a non-elementary, analytically finite Kleinian group and they agree with the classical Poincaré exponent. Oblatum 30-X-1995 & 11-III-1996