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By Mr (a: F (f, Kurt (ch-bern-im) Stratmann and Bernd O. (-stan


Constructing restricted Patterson measures for geometrically infinite Kleinian groups. (English summary) Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 2, 431–446. In this paper, the focus of which is on geometrically infinite Kleinian groups, the authors study exhaustions of such groups by specific subsets which have properties reminiscent of geometrically finite groups. Each of these subsets (the authors call them ρ-restrictions) defines a ρ-restricted limit set which is a closed subset of the limit set of the original group and which carries a (ρ-restricted) Patterson-Sullivan measure. This ρ-restricted Patterson-Sullivan measure shows similarities with the classical Patterson-Sullivan measure for geometrically finite Kleinian groups. The exponent of convergence of the ρ-restriction agrees with the Hausdorff dimension of the ρ-restricted limit set, and the Poincaré series of the ρ-restriction diverges at the critical exponent. Furthermore, as ρ → ∞, the exponent of convergence of the ρ-restriction converges to the exponent of convergence of the original group. Reviewed by Petra Bonfert-Taylo

Year: 2011
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