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Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 299))

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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).

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© 1992 Springer-Verlag Berlin Heidelberg

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Pommerenke, C. (1992). Quasidisks. In: Boundary Behaviour of Conformal Maps. Grundlehren der mathematischen Wissenschaften, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02770-7_5

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  • DOI: https://doi.org/10.1007/978-3-662-02770-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08129-3

  • Online ISBN: 978-3-662-02770-7

  • eBook Packages: Springer Book Archive

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