#### Volume 14, issue 1 (2010)

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Kleinian groups of small Hausdorff dimension are classical Schottky groups. I

### Yong Hou

Geometry & Topology 14 (2010) 473–519
##### Abstract

It has been conjectured that the Hausdorff dimensions of nonclassical Schottky groups are strictly bounded from below. In this first part of our work on this conjecture, we prove that there exists a universal positive number $\lambda$ greater than $0$ such that any $2$–generated nonelementary Kleinian group with limit set of Hausdorff dimension less than $\lambda$ is a classical Schottky group.

##### Keywords
Schottky group, Kleinian group, Hausdorff dimension, limit set
##### Mathematical Subject Classification 2000
Primary: 57M50, 57M05
Secondary: 53C21, 53C20, 37A15