About one problem on extremal decomposition

Ya. Zabolotnii, I. Denega

Institute of Mathematics of the National Academy of Sciences of Ukraine, 3, Tereschenkivska st., Kyiv-4 01024, Ukraine

Abstract: In the paper, we consider an open problem of finding the maximum of product of inner radii of mutually non-overlapping domains with respect to the points of the unit circle on a certain positive degree $\gamma$ of the inner radius of the domain with respect to the origin, moreover, the domain containing origin does not intersect with other domains.

Keywords: inner radius of the domain, mutually non-overlapping domains, the Green function, quadratic differential, the Dubinin problem.

UDC: 517.54

MSC: 30C75

Received: 10.06.2021
Revised: 26.07.2021
Accepted: 08.08.2021

Language: English

DOI: 10.15393/j3.art.2021.10410

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