Quasidisks

  • Christian Pommerenke
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 299)

Abstract

A quasicircle in ℂ is a (not necessarily rectifiable) Jordan curve J such that
$$ diam\;J(a,b) \leqslant M|a - b|\;for\;a,b \in J$$
where J(a, b) is the smaller arc of J between a and b. The inner domain is called a quasidisk. This important concept was introduced by Ahlfors and appears in many different contexts (see e.g. Geh87).

Keywords

Prool 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Christian Pommerenke
    • 1
  1. 1.Fachbereich MathematikTechnische UniversitätBerlin 12Germany

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