Groups, Geometry, and Dynamics
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Published online: 2013-01-31
Combinatorial modulus, the combinatorial Loewner property, and Coxeter groupsMarc Bourdon and Bruce Kleiner (1) Université Lille I, Villeneuve d'Ascq, France
(2) Courant Institute of Mathematical Sciences, New York, United States
We study combinatorial modulus on self-similar metric spaces. We give new examples of hyperbolic groups whose boundaries satisfy a combinatorial version of the Loewner property, and prove Cannon’s conjecture for Coxeter groups. We also establish some connections with $\ell_p$-cohomology.
Keywords: Geometric group theory, hyperbolic groups and nonpositively curved groups, quasiconformal mappings in metric spaces
Bourdon Marc, Kleiner Bruce: Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups. Groups Geom. Dyn. 7 (2013), 39-107. doi: 10.4171/GGD/177