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

Hou, Yong

doi:10.2140/gt.2010.14.473

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

Yong Hou

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 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

Volume 14, issue 1 (2010)