Geodesic
Versions of Koebe 1/4 Theorem for Analytic and Quasiregular Harmonic Functions and Applications
Publications de l'Institut Mathématique, _N_S_84 (2008) no. 98, p. 61 .

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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.
DOI : 10.2298/PIM0898061M
Classification : 30C62 30C35 
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     title = {Versions of {Koebe} 1/4 {Theorem} for {Analytic} and {Quasiregular} {Harmonic} {Functions} and {Applications}},
     journal = {Publications de l'Institut Math\'ematique},
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Miodrag Mateljević. Versions of Koebe 1/4 Theorem for Analytic and Quasiregular Harmonic Functions and Applications. Publications de l'Institut Mathématique, _N_S_84 (2008) no. 98, p. 61 . doi : 10.2298/PIM0898061M. http://geodesic.mathdoc.fr/articles/10.2298/PIM0898061M/

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