%A A. L. Targonskii %A I. Targonskaya %J International Journal of Advanced Research in Mathematics %T On the one extremal problem on the Riemann sphere %X Sharp estimates of product of inner radii for pairwise disjoint domains are obtained. In particular, we solve an extremal problem in the case of arbitrary finite number of rays containing arbitrary even number of free poles %N 4 %K Inner radius of domain, quadratic differential, piecewise-separating transformation, Green function, radial systems of points, logarithmic capacity, variational formula %P 1-7 %D 2016 %I SciPress Ltd., Switzerland %L zu220629