Combinatorial modulus, the Combinatorial Loewner Property, and Coxeter groups

TL;DR

This paper explores the combinatorial modulus on hyperbolic Coxeter group boundaries, introduces new examples satisfying a combinatorial Loewner property, proves Cannon's conjecture for Coxeter groups, and links these concepts to l^p cohomology.

Contribution

It provides new examples of hyperbolic groups with boundary satisfying a combinatorial Loewner property and proves Cannon's conjecture for Coxeter groups.

Findings

Established combinatorial Loewner property for new hyperbolic group examples

Proved Cannon's conjecture for Coxeter groups

Connected combinatorial modulus with l^p cohomology

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.