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.

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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. 
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     author = {Miodrag Mateljevi\'c},
     title = {Versions of {Koebe} 1/4 {Theorem} for {Analytic} and {Quasiregular} {Harmonic} {Functions} and {Applications}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {61 - 72},
     publisher = {mathdoc},
     volume = {(N.S.) 84},
     number = {98},
     year = {2008},
     zbl = {1274.30089},
     url = {https://geodesic-test.mathdoc.fr/item/PIM_2008_N_S_84_98_a3/}
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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. https://geodesic-test.mathdoc.fr/item/PIM_2008_N_S_84_98_a3/