Hausdorff dimension of boundaries of relatively hyperbolic groups
Geometric Topology
2019-06-26 v2 Group Theory
Abstract
In this paper, we study the Hausdorff dimension of the Floyd and Bowditch boundaries of a relatively hyperbolic group, and show that for the Floyd metric and shortcut metrics respectively, they are are both equal to a constant times the growth rate of the group. In the proof, we study a special class of conical points called uniformly conical points and establish that, in both boundaries, there exists a sequence of Alhfors regular sets with dimension tending to the Hausdorff dimension and these sets consist of uniformly conical points.
Keywords
Cite
@article{arxiv.1609.01763,
title = {Hausdorff dimension of boundaries of relatively hyperbolic groups},
author = {Leonid Potyagailo and Wen-yuan Yang},
journal= {arXiv preprint arXiv:1609.01763},
year = {2019}
}