Geometry & Topology

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

Yong Hou

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.

Article information

Source
Geom. Topol., Volume 14, Number 1 (2010), 473-519.

Dates
Revised: 6 May 2009
Accepted: 23 September 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732180

Digital Object Identifier
doi:10.2140/gt.2010.14.473

Mathematical Reviews number (MathSciNet)
MR2578309

Zentralblatt MATH identifier
1188.30053

Citation

Hou, Yong. Kleinian groups of small Hausdorff dimension are classical Schottky groups. I. Geom. Topol. 14 (2010), no. 1, 473--519. doi:10.2140/gt.2010.14.473. https://projecteuclid.org/euclid.gt/1513732180

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