The problem of extremal decomposition of a complex plane with free poles on a circle

Abstract

In this paper, the problem concerning the maximum product of the inner radii of $n$ mutually non-overlapping domains symmetric with respect to a unit circle and the inner radius of some domain with respect to the zero raised to a positive degree $\gamma$ is studied. The problem has been solved for $n=\overline{4,7}$ and some $\gamma>1$.