All finitely generated Kleinian groups of small Hausdorff dimension are classical Schottky groups

2013/07/10 by Hou, Yong
#53 #57 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1307.2677

Abstract

This is the second part of the works on Hausdorff dimensions of Schottky groups. It has been conjectured that the Hausdorff dimensions of nonclassical Schottky groups are strictly bounded from below. In this second part of our works we provide a resolution of this conjecture, we prove that there exists a universal positive number λ>0, such that any finitely-generated non-elementary Kleinian groups with limit set of Hausdorff dimension

Related

• The classification of Kleinian groups of Hausdorff dimensions at most one
• The classification of Kleinian groups of Hausdorff dimensions at most one and Burnside's conjecture
• Hausdorff dimension of non-conical limit sets
• Variation of the Hausdorff dimension and degenerations of Schottky groups
• Homological dimension and critical exponent of Kleinian groups