The Discontinuity Function of Discrete Groups and Radius of Schlichtness

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Abstract

We define the notion of the discontinuity radius of a discrete and discontinuous group. This is a function which is closely related to the group geometry. We demonstrate the usefullness of this notion by proving some geometrical results and by computing the schlichtness radius of certain Blaschke products. In a subsequent paper we will give further applications to Fuchsian groups.

Original languageEnglish
Pages (from-to)1189-1198
Number of pages10
JournalComplex Analysis and Operator Theory
Volume6
Issue number6
DOIs
StatePublished - 1 Dec 2012

Keywords

  • Discontinuous groups
  • Discrete groups
  • Schlichtness radius of analytic functions

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