EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 84(98), pp. 61–72 (2008)

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VERSIONS OF KOEBE 1/4 THEOREM FOR ANALYTIC AND QUASIREGULAR HARMONIC FUNCTIONS AND APPLICATIONS

Miodrag Mateljevic

Matematicki fakultet, Beograd, Serbia

Abstract: In this paper we mainly survey results obtained in [MM3]. For example, we give an elementary proof of two versions of Koebe $1/4$ theorem for analytic functions (see Theorem 1.2 and Theorem 1.4 below). We also show a version of the Koebe theorem for quasiregular harmonic functions. As an application, we show that holomorphic functions (more generally quasiregular harmonic functions) and their modulus have similar behavior in a certain sense.

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Electronic fulltext finalized on: 9 Dec 2008. This page was last modified: 12 Dec 2008.

© 2008 Mathematical Institute of the Serbian Academy of Science and Arts
© 2008 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition