Computational Methods and Function Theory 2 (2002), No. 2, 469--479
Copyright Heldermann Verlag 2002
Katsuhiko Matsuzaki
matsuzak@math.ocha.ac.jp, Department of Mathematics, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan.
For a non-elementary Kleinian group $G$ acting on an $n$-dimensional sphere, we consider a conformally invariant probability measure of the dimension at the critical exponent of the Poincar\'e series. When this diverges, such a measure is unique and it is called the Patterson-Sullivan measure. We prove that the action of any non-trivial normal subgroup $\Gamma$ of $G$ is conservative with respect to the Patterson-Sullivan measure for $G$.
Keywords: Kleinian group, critical exponent, divergence type, conical limit set, conformally invariant measure, conservative part, horospherical limit set.
MSC 2000: 30F40.
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