THE PATTERSON MEASURE FOR GEOMETRICALLY FINITE-GROUPS WITH PARABOLIC ELEMENTS, NEW AND OLD

We study the Patterson measure on the limit set of a geometrically finite Kleinian group with parabolic elements. Using the delta-conformality of the Patterson measure in combination with basic hyperbolic geometry we obtain a global Shadow Lemma. This macroscopic measure estimate is exploited to derive a Khintchine-type theorem, which is then used for a finer analysis of the density of the limit set in terms of Hausdorff measure.