Combinatorial modulus, the Combinatorial Loewner Property, and Coxeter groups

2010/02/09 by Marc Bourdon, Bruce Kleiner, Bourdon, Marc +1
Mathematics · #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #math.DG #math.GR #math.MG

paper · pdf · doi:10.48550/arxiv.1002.1991

openalex publication_date 2010/02/09 · arxiv created 2011/05/03 · arxiv updated 2011/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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