%A A. L. Targonskii %J International Journal of Advanced Research in Mathematics %T On the One Extremal Problem with the Free Poles on the Unit circle %X The sharp estimates of the product of the inner radius for pairwise disjoint domains are obtained. In particular, we solve an extremal problem in the case of an arbitrary finite number of the free poles on the unit circle for the following functional %N 6 %K inner radius of domain, quadratic differential, piecewise-separating transformation, Green function, radial systems of points, logarithmic capacity, variational formula %P 26-31 %D 2016 %I SciPress Ltd., Switzerland %L zu225118