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ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2021, том 12, номер 4, страницы 82–91 (Mi emj424)

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

Аннотация: 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.

Ключевые слова и фразы: inner radius of the domain, mutually non-overlapping domains, the Green function, quadratic differential, the Goluzin theorem.

MSC: 30C75

Поступила в редакцию: 01.06.2020

Язык публикации: английский

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



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