On local behavior of mappings with unbounded characteristic
- Authors: Sevost’yanov E.1
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Affiliations:
- Zhytomyr State University
- Issue: Vol 38, No 2 (2017)
- Pages: 371-378
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199124
- DOI: https://doi.org/10.1134/S1995080217020202
- ID: 199124
Cite item
Abstract
This article is a survey of the earlier results of the author. We study space mappings with branching that satisfy modulus inequalities. For classes of these mappings, we obtain several sufficient conditions for the normality of families. Moreover, we prove that the normal families of the so-called Q-mappings have the logarithmic order of growth in a neighborhood of a point. We obtain a result on the normal families of open discrete mappings f: D → C {a, b} from the class Wloc1,1 with finite distortion that do not take at least two fixed values a ≠ b in C whose maximal dilatation has a majorant of finite mean oscillation at every point. This result is an analog of the well-known Montel theorem for analytic functions.
About the authors
E. Sevost’yanov
Zhytomyr State University
Author for correspondence.
Email: esevostyanov2009@mail.ru
Ukraine, ul. Bol’shaya Berdichevskaya 40, Zhytomyr, 10 008