Conformal dimension of hyperbolic groups that split over elementary subgroups

• 成果类型: Article
• 署名作者: Carrasco, Matias; Mackay, John M.
• 署名单位: Universidad de la Republica, Uruguay; University of Bristol
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01074-w
• 发表日期: 2022
• 页码: 795-854
• 关键词: canonical splittings; accessibility; planes

摘要

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 2-torsion) have conformal dimension 1, answering a question of Bonk and Kleiner.