Extremal decomposition problem for the complex plane with free poles on the circle

Keywords: inner radius of a domain, non-overlapping domains, extremal problems for non-overlapping domains, systems of points of a circle, separating transformation

Abstract

UDC 517.9

We consider the problem of maximization of the product of inner radii of $n$ nonoverlapping domains, which are symmetric with respect to the unit circle, and the inner radius to the power $\gamma$ of a domain with respect to zero. We solve the problem for $n=2$ and $n=3$ and some $\gamma>1.$

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Published
24.12.2020
How to Cite
Bakhtin , O. K., L. V. Vyhivska, and I. V. Denega. “Extremal Decomposition Problem for the Complex Plane With Free Poles on the Circle”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 12, Dec. 2020, pp. 1599-20, doi:10.37863/umzh.v72i12.6216.
Section
Research articles