Conformal dimension of hyperbolic groups that split over elementary subgroups
Metric Geometry
2022-08-23 v2 Classical Analysis and ODEs
Group Theory
Abstract
We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without -torsion) have conformal dimension 1, answering a question of Bonk and Kleiner.
Cite
@article{arxiv.2007.09030,
title = {Conformal dimension of hyperbolic groups that split over elementary subgroups},
author = {Matias Carrasco and John M. Mackay},
journal= {arXiv preprint arXiv:2007.09030},
year = {2022}
}
Comments
v1: 47 pages, 6 figures; v2: 48 pages, 6 figures, minor changes to introduction