Antoine Clais

Abstract of the talk of Antoine Clais

CLP on boundaries of right-angled hyperbolic buildings.

Recently, a combinatorial approach have been developed to study quasiconformal structures of boundaries of hyperbolic groups. The motivation of this is to be able to characterize the regularity of a boundary that does not come with a good measure. Some how this can be done thanks to the Combinatorial Loewner Property (CLP). The CLP is a discrete version of the Loewner Property introduced by Heinonen and Koskela in abstract metric measured spaces. The CLP have been used for instance by M. Bourdon and B. Kleiner to give a new proof of the Cannon conjecture for Coxeter groups. In this talk I will give an overview of this theory and present an example of right-angled hyperbolic building of dimension 3 whose boundary satisfy the CLP.