On extremal decomposition problems

We adapt the capacity approach and symmetrization method to some extremal decomposition problems on the disk unit or an annulus. We consider the problems on the maximum product of the inner radii of pairwise disjoint domains and the maximum product of the Robin radii of such domains. The new invariants with respect to Möbius transformations of the Riemann sphere are introduced. In particular, for these invariants the problems on extremal decomposition with free poles on the unit circle are investigated. Bibl. – 19 titles.