Volume 14, issue 1 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 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 2000
Primary: 57M50, 57M05
Secondary: 53C21, 53C20, 37A15
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
Yong Hou
Department of Mathematics
North Dakota State University
Fargo, ND 58108
USA