On the Hausdorff dimension distortions of quasi-symmetric homeomorphisms

Authors

  • Shengjin Huo Tiangong University, Department of Mathematics

Keywords:

Conical limit set, escaping geodesic, compact deformation

Abstract

 

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'.
Section
Articles

Published

2022-07-01

How to Cite

Huo, S. (2022). On the Hausdorff dimension distortions of quasi-symmetric homeomorphisms. Annales Fennici Mathematici, 47(2), 927–938. https://doi.org/10.54330/afm.120510