Hausdorff dimension of boundaries of relatively hyperbolic groups

Potyagailo, Leonid; Yang, Wen-yuan

doi:10.2140/gt.2019.23.1779

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Hausdorff dimension of boundaries of relatively hyperbolic groups

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Potyagailo, Leonid
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.2140/gt.2019.23.1779
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Citation

Potyagailo, L., & Yang, W.-y. (2019). Hausdorff dimension of boundaries of relatively hyperbolic groups. Geometry & Topology, 23(4), 1779-1840. doi:10.2140/gt.2019.23.1779.

Cite as: https://hdl.handle.net/21.11116/0000-0004-C6BD-8

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.