On horospheric limit sets of Kleinian groups

  • Kurt Falk

    Christian-Albrechts-Universität zu Kiel, Germany
  • Katsuhiko Matsuzaki

    Waseda University, Tokyo, Japan
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Abstract

In this paper we partially answer a question of P. Tukia about the size of the difference between the big horospheric limit set and the horospheric limit set of a Kleinian group. We mainly investigate the case of normal subgroups of Kleinian groups of divergence type and show that this difference is of zero conformal measure by using another result obtained here: the Myrberg limit set of a non-elementary Kleinian group is contained in the horospheric limit set of any non-trivial normal subgroup.

Cite this article

Kurt Falk, Katsuhiko Matsuzaki, On horospheric limit sets of Kleinian groups. J. Fractal Geom. 7 (2020), no. 4, pp. 329–350

DOI 10.4171/JFG/93