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arXiv · 1404.4896

Analog of Montel theorem for mappings of Sobolev class with finite distortion

Evgeny Sevost'yanov
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Abstract

The present paper is devoted to the study of classes of mappings with non-bounded characteristic of quasiconformality. It is obtained a result on normal families of the open discrete mappings $f:D\rightarrow {\Bbb C}\setminus\{a, b\}$ of the class $W_{loc}^{1, 1}$ having a finite distortion and omitting two fixed values $a\ne b$ in ${\Bbb C},$ maximal dilatations of which has a majorant of the class of finite mean oscillation at every point. In particular, the result mentioned above holds for the so-called $Q$-mappings and is an analog of known Montel theorem for analytic functions.

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Evgeny Sevost'yanov. 2014-04-18. Analog of Montel theorem for mappings of Sobolev class with finite distortion. https://arxiv.org/abs/1404.4896

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