Generalized Reduced Module of a Domain Over the Unit Disc with Circular and Radial Slits
- Authors: Elizarov A.M.1, Kazantsev A.V.1, Kinder M.I.1
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Affiliations:
- Kazan (Volga region) Federal University
- Issue: Vol 39, No 5 (2018)
- Pages: 664-672
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202200
- DOI: https://doi.org/10.1134/S1995080218050074
- ID: 202200
Cite item
Abstract
For (n + 1)-ly connected planar domain D with analytic boundary we construct the function F(w,w0) = (w − w0)f(w,w0) which maps D conformally onto the unit disk with circular and radial slits. We show that if n ≥ 2, then Mityuk’s function, M(w) = −(2π)−1 ln |f(w,w)|, representing the generalized reduced module of the domain D has at least one stationary point in D.
About the authors
A. M. Elizarov
Kazan (Volga region) Federal University
Author for correspondence.
Email: amelizarov@gmail.com
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008
A. V. Kazantsev
Kazan (Volga region) Federal University
Email: amelizarov@gmail.com
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008
M. I. Kinder
Kazan (Volga region) Federal University
Email: amelizarov@gmail.com
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008