an:01821263
Zbl 1013.30024
Bonfert-Taylor, Petra; Taylor, Edward C.
Quasiconformal groups, Patterson-Sullivan theory, and local analysis of limit sets
EN
Trans. Am. Math. Soc. 355, No. 2, 787-811 (2003).
00089622
2003
j
30F40 30F45 30C65
Kleinian groups; discrete quasi-conformal groups; Patterson-Sullivan measure; exponent of convergence; Hausdorff dimension
The authors extend some aspects of the Patterson-Sullivan theory, that is, the construction of a class of finite positive measures on the limit set of a Kleinian group and the relation between the exponent of convergence of the Poincar?? series of the action and the Hausdorff dimension of the limit set. The extension concerns the setting of quasiconformal Fuchsian groups, that is, discrete groups of uniformly \(K\)-quasi-conformal mappings preserving the closed unit ball \(B^n\). In doing so, the authors define some new bi-Lipschitz invariants that localize both the exponent of convergence and the Hausdorff dimension.
Athanase Papadopoulos (Strasbourg)