Conformal radius: At the interface of traditions
- 作者: Kazantsev A.1
-
隶属关系:
- Kazan (Volga Region) Federal University
- 期: 卷 38, 编号 3 (2017)
- 页面: 469-475
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199261
- DOI: https://doi.org/10.1134/S1995080217030167
- ID: 199261
如何引用文章
详细
H. Behnke’s and E. Peschl’s definition of plänarkonvexitat leads to the Epstein-type inequalities when applies to the Hartogs domains in C2. One-parameter series of such inequalities reveals the following rigidity phenomenon: the set of the parameters with contensive inequalities is exactly the segment which center corresponds to the well-known Nehari ball. The latter plays the crucial role in the forming the Gakhov class of all holomorphic and locally univalent functions in the unit disk with no more than one-pointed null-sets of the gradients of their conformal radii. The sufficient condition for the piercing of the Nehari sphere out of the Gakhov class is found. We deduce such a condition along the lines of the subordination approach to the proof of Haegi’s theorem about the inclusion of any convex holomorphic function into the Gakhov class.
作者简介
A. Kazantsev
Kazan (Volga Region) Federal University
编辑信件的主要联系方式.
Email: avkazantsev63@gmail.com
俄罗斯联邦, ul. Kremlevskaya 18, Kazan, 420008
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