Abstract
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, they 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.
Citation
Leonid Potyagailo. Wen-yuan Yang. "Hausdorff dimension of boundaries of relatively hyperbolic groups." Geom. Topol. 23 (4) 1779 - 1840, 2019. https://doi.org/10.2140/gt.2019.23.1779
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