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JOURNALS // Problemy Analiza — Issues of Analysis // Archive

Probl. Anal. Issues Anal., 2020 Volume 9(27), Issue 1, Pages 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.

Abstract: 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.

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

UDC: 517.54

MSC: 30C75

Received: 22.10.2019
Accepted: 07.01.2020

Language: English

DOI: 10.15393/j3.art.2020.7190



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