Geometry & Topology
- Geom. Topol.
- Volume 14, Number 1 (2010), 473-519.
Kleinian groups of small Hausdorff dimension are classical Schottky groups. I
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 greater than such that any –generated nonelementary Kleinian group with limit set of Hausdorff dimension less than is a classical Schottky group.
Geom. Topol., Volume 14, Number 1 (2010), 473-519.
Received: 17 March 2008
Revised: 6 May 2009
Accepted: 23 September 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds 57M05: Fundamental group, presentations, free differential calculus
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 37A15: General groups of measure-preserving transformations [See mainly 22Fxx]
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