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The Miniowitz and Vuorinen theorems for the mappings with non-bounded characteristics

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Abstract

The paper is devoted to the study of classes of mappings with non-bounded characteristics of quasiconformality. We prove that the normal families of Q-mappings have the logarithmic order of growth in a neighborhood of a point. Moreover, we establish sufficient conditions for Q to ensure the normality of mappings f: D → , n ≥ 2, which omit the points of a set E f . The latter obeys c(E f ) ≥ δ, δ > 0, where c(·) is an appropriate set function.

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  1. Zhitomir Ivan Franko State University, 40 Bol’shaya Berdichevskaya Str., Zhitomir, 10 008, Ukraine

    Evgeny Sevost’yanov

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  1. Evgeny Sevost’yanov
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Correspondence to Evgeny Sevost’yanov.

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Sevost’yanov, E. The Miniowitz and Vuorinen theorems for the mappings with non-bounded characteristics. Isr. J. Math. 209, 527–545 (2015). https://doi.org/10.1007/s11856-015-1228-y

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  • DOI: https://doi.org/10.1007/s11856-015-1228-y

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