Hausdorff dimension of boundaries of relatively hyperbolic groups

Potyagailo, Leonid¹ ; Yang, Wen-yuan²

¹ UFR de Mathématiques, Université de Lille 1, Villeneuve d’Ascq, France
² Beijing International Center for Mathematical Research & School of Mathematical Sciences, Peking University, Beijing, China

Geometry & topology, Tome 23 (2019) no. 4, pp. 1779-1840.

Résumé

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.

Détail

DOI : 10.2140/gt.2019.23.1779

Classification : 20F65, 20F67
Keywords: Floyd boundary, Hausdorff dimension, growth rate, conical points, Ahlfors-regular

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