Geometry & Topology 14 (2010) 473–519

DOI: 10.2140/gt.2010.14.473

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 λ greater than 0 such that any 2–generated nonelementary Kleinian group with limit set of Hausdorff dimension less than λ is a classical Schottky group.

Keywords

Schottky group, Kleinian group, Hausdorff dimension, limit set

Mathematical Subject Classification

Primary: 57M05, 57M50

Secondary: 37A15, 53C20, 53C21

References

Publication

Received: 17 March 2008
Revised: 6 May 2009
Accepted: 23 September 2009
Preview posted: 31 October 2009
Published: 2 January 2010
Proposed: Benson Farb
Seconded: Walter Neumann, Joan Birman

Authors