Open Access
Translator Disclaimer
2010 Kleinian groups of small Hausdorff dimension are classical Schottky groups. I
Yong Hou
Geom. Topol. 14(1): 473-519 (2010). 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.

Citation

Download Citation

Yong Hou. "Kleinian groups of small Hausdorff dimension are classical Schottky groups. I." Geom. Topol. 14 (1) 473 - 519, 2010. https://doi.org/10.2140/gt.2010.14.473

Information

Received: 17 March 2008; Revised: 6 May 2009; Accepted: 23 September 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1188.30053
MathSciNet: MR2578309
Digital Object Identifier: 10.2140/gt.2010.14.473

Subjects:
Primary: 57M05 , 57M50
Secondary: 37A15 , 53C20 , 53C21

Keywords: Hausdorff dimension , Kleinian group , limit set , Schottky group

Rights: Copyright © 2010 Mathematical Sciences Publishers

JOURNAL ARTICLE
47 PAGES


SHARE
Vol.14 • No. 1 • 2010
MSP
Back to Top