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ЖУРНАЛЫ // Проблемы анализа — Issues of Analysis // Архив

Пробл. анал. Issues Anal., 2020, том 9(27), выпуск 1, страницы 60–65 (Mi pa288)

Estimate of the maximum product of inner radii of non-overlapping domains

Iryna Denega

Institute of Mathematics of the National Academy of Sciences of Ukraine, Department of complex analysis and potential theory, 01024 Ukraine, Kyiv-4, 3, Tereschenkivska st.

Аннотация: In this paper, the upper estimate for the maximum of the products of inner radii of mutually non-overlapping domains is obtained for any $n$-radial system of points on the complex plane at all possible values of some parameter $\gamma$. The conditions under which the structure of points is not important in the proved results are established.

Ключевые слова: inner radius of domain, non-overlapping domains, the Green function, transfinite diameter, theorem on minimizing of the area, the Cauchy inequality.

УДК: 517.54

MSC: 30C75

Поступила в редакцию: 22.10.2019
Принята в печать: 07.01.2020

Язык публикации: английский

DOI: 10.15393/j3.art.2020.7190



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