paper

Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity

arXiv:1009.0468

Abstract

The main result of this paper is to show that if $\H$ is a normal subgroup of a Kleinian group such that $G/\H$ contains a coset which is represented by some loxodromic element, then the Hausdorff dimension of the transient limit set of $\H$ coincides with the Hausdorff dimension of the limit set of . This observation extends previous results by Fernández and Melián for Riemann surfaces.

11 pages, 3 figures

Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity · wovepaper