Conformal dimension and Gromov hyperbolic groups with 2–sphere boundary

2002/08/31 by Mario Bonk, Bruce Kleiner · 2 citations
Mathematics · #Boundary (topology) #Conformal map #Dimension (graph theory) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Group (periodic table) #Hyperbolic 3-manifold #Hyperbolic function #Hyperbolic group #Hyperbolic manifold #Hyperbolic space #Hyperbolic triangle #Infinity #Kleinian group #Mathematical analysis #Mathematics #Metric (unit) #Physics #Pure mathematics #Relatively hyperbolic group #Space (punctuation) #math.GR #math.GT #math.MG #msc:20F67 #msc:30C65

paper · pdf · doi:10.2140/gt.2005.9.219

published as Geom. Topol. 9 (2005) 219-246 · Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper7.abs.html

openalex publication_date 2005/01/26 · arxiv created 2005/02/15 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Suppose G is a Gromov hyperbolic group, and G is quasisymmetrically homeomorphic to an Ahlfors Q-regular metric 2-sphere Z with Ahlfors regular conformal dimension Q. Then G acts discretely, cocompactly, and isometrically on

Citations

• Quasisymmetric parametrizations of two-dimensional metric spheres
• The density at infinity of a discrete group of hyperbolic motions
• Quasiconformal maps in metric spaces with controlled geometry

Cited by

• Combinatorial Modulus on Boundary ofRight-Angled Hyperbolic Buildings
• Uniformization of cofat domains on metric two-spheres
• Geometric group theory [wikipedia]