Geodesic
Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups
Marc Bourdon1 ; Bruce Kleiner2
1Université Lille I, Villeneuve d'Ascq, France
2Courant Institute of Mathematical Sciences, New York, United States
Groups, geometry, and dynamics, Tome 7 (2013) no. 1, pp. 39-107

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DOI

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 lp​-cohomology.
DOI : 10.4171/ggd/177
Classification : 20-XX, 30-XX, 00-XX
Mots-clés : Geometric group theory, hyperbolic groups and nonpositively curved groups, quasiconformal mappings in metric spaces

Marc Bourdon  1   ; Bruce Kleiner  2

1 Université Lille I, Villeneuve d'Ascq, France
2 Courant Institute of Mathematical Sciences, New York, United States 
Marc Bourdon; Bruce Kleiner. Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups. Groups, geometry, and dynamics, Tome 7 (2013) no. 1, pp. 39-107. doi: 10.4171/ggd/177
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     title = {Combinatorial modulus, the combinatorial {Loewner} property, and {Coxeter} groups},
     journal = {Groups, geometry, and dynamics},
     pages = {39--107},
     year = {2013},
     volume = {7},
     number = {1},
     doi = {10.4171/ggd/177},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/177/}
}
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