Groups, Geometry, and Dynamics


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Volume 7, Issue 1, 2013, pp. 39–107
DOI: 10.4171/GGD/177

Published online: 2013-01-31

Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups

Marc Bourdon[1] and Bruce Kleiner[2]

(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