Tohoku Mathematical Journal
2004
December
SECOND SERIES VOL. 56, NO. 4

Tohoku Math. J.
56 (2004), 553-569

Title REMARKS ON HAUSDORFF DIMENSIONS FOR TRANSIENT LIMIT SETS OF KLEINIAN GROUPS

Author Kurt Falk and Bernd O. Stratmann

(Received March 31, 2003, revised April 27, 2004)
Abstract. In this paper we study normal subgroups of Kleinian groups as well as discrepancy groups (d-groups), that are Kleinian groups for which the exponent of convergence is strictly less than the Hausdorff dimension of the limit set. We show that the limit set of a d-group always contains a range of fractal subsets, each containing the set of radial limit points and having Hausdorff dimension strictly less than the Hausdorff dimension of the whole limit set. We then consider normal subgroups $G$ of an arbitrary non-elementary Kleinian group $H$, and show that the exponent of convergence of $G$ is bounded from below by half of the exponent of convergene of $H$. Finally, we give a discussion of various examples of d-groups.

2000 Mathematics Subject Classification. Primary 30F40; Secondary 37F35.
Key words and phrases. Kleinian groups, exponent of convergence, fractal geometry.

To the top of this page

Back to the Contents