Combinatorial modulus, the Combinatorial Loewner Property, and Coxeter groups

Marc Bourdon, Bruce Kleiner

Published 2010-02-09, updated 2011-05-03Version 2

We study combinatorial modulus on boundaries of hyperbolic Coxeter groups. We give new examples of hyperbolic groups whose boundary satisfies a combinatorial version of the Loewner property, and prove Cannon's conjecture for Coxeter groups. We also establish some connections with l^p cohomology.