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Hausdorff dimension of
boundaries of relatively hyperbolic groups
Leonid Potyagailo and Wen-yuan Yang |
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Geometry & Topology 23 (2019) 1779–1840
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Abstract |
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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. |
Keywords
Floyd boundary, Hausdorff dimension, growth rate, conical
points, Ahlfors-regular
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Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F67
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References |
Publication
Received: 28 November 2016
Revised: 13 June 2018
Accepted: 7 October 2018
Published: 17 June 2019
Proposed: Jean-Pierre Otal
Seconded: Dmitri Burago, Leonid Polterovich
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Authors |
| Leonid Potyagailo | |
| UFR de Mathématiques Université de Lille 1 Villeneuve d’Ascq France |
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| Wen-yuan Yang | |
| Beijing International Center for
Mathematical Research & School of Mathematical
Sciences Peking University Beijing China |
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