On horospheric limit sets of Kleinian groups

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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.

Original languageEnglish
Pages (from-to)329-350
Number of pages22
JournalJournal of Fractal Geometry
Volume7
Issue number4
DOIs
Publication statusPublished - 2020

Keywords

  • Critical exponent
  • Geodesic flow
  • Hausdorff dimension
  • Horospheric limit set
  • Kleinian group
  • Myrberg limit set
  • Patterson measure

ASJC Scopus subject areas

  • Geometry and Topology
  • Applied Mathematics

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