Conformal dimension and canonical splittings of hyperbolic groups

Abstract

We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic groups and show an interesting relationship between conformal dimension and some canonical splittings of the group.

arXiv comment19 pages, 1 figure. This is a revised version, containing more details and the main ideas of the proofs. The notations were also simplified