Geodesic
On the Hausdorff dimension distortions of quasi-symmetric homeomorphisms
Shengjin Huo1
1Tiangong University, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 927-938

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  In this paper, we first prove that for a Fuchsian group $G$ of divergence type and non-lattice, if $h$ is a quasi-symmetric homeomorphism of the real axis $\mathbb{R}$ corresponding to a quasi-conformal compact deformation of $G$, then $h$ is not strongly singular for divergence groups. This generalizes a result of Bishop and Steger (1993). Furthermore, we show that Bishop and Steger's result does not hold for the covering groups of all $d$-dimensional 'Jungle Gyms' ($d$ is any positive integer) which generalizes Gönye's results (2007) where the author discussed the case of 1-dimensional 'Jungle Gym'.
DOI : 10.54330/afm.120510
Keywords: Conical limit set, escaping geodesic, compact deformation

Shengjin Huo  1

1 Tiangong University, Department of Mathematics 
Shengjin Huo. On the Hausdorff dimension distortions of quasi-symmetric homeomorphisms. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 927-938. doi: 10.54330/afm.120510
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