On local behavior of mappings with unbounded characteristic
- 作者: Sevost’yanov E.1
-
隶属关系:
- Zhytomyr State University
- 期: 卷 38, 编号 2 (2017)
- 页面: 371-378
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199124
- DOI: https://doi.org/10.1134/S1995080217020202
- ID: 199124
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详细
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.
作者简介
E. Sevost’yanov
Zhytomyr State University
编辑信件的主要联系方式.
Email: esevostyanov2009@mail.ru
乌克兰, ul. Bol’shaya Berdichevskaya 40, Zhytomyr, 10 008