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JOURNALS // Eurasian Mathematical Journal // Archive

Eurasian Math. J., 2021 Volume 12, Number 4, Pages 82–91 (Mi emj424)

This article is cited in 3 papers

An extremal problem on non-overlapping domains containing ellipse points

Ya. V. Zabolotnii, I. V. Denega

Department of complex analysis and potential theory, Institute of mathematics of the National Academy of Sciences of Ukraine, 3 Tereschenkivska St, 01024 Kyiv, Ukraine

Abstract: An extremal problem of geometric function theory of a complex variable for the maximum of products of the inner radii on a system of $n$ mutually non-overlapping multiply connected domains $B_k$ containing the points $a_k$, $k=\overline{1,n}$, located on an arbitrary ellipse $\frac{x^2}{d^2}+\frac{y^2}{t^2}=1$ for which $d^2-t^2=1$, is solved.

Keywords and phrases: inner radius of the domain, mutually non-overlapping domains, the Green function, quadratic differential, the Goluzin theorem.

MSC: 30C75

Received: 01.06.2020

Language: English

DOI: 10.32523/2077-9879-2021-12-4-82-91



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