On extremal decomposition of $n$-space domains

Classical results by Lavrent'ev, Alenitsyn, and Kufarev on the product of the conformal radii of planar nonoverlapping domains, as well as a recent result on an extremal decomposition with free poles on the circle are extended to the case of domains in the $n$-dimensional Euclidean space, $n>3$, with conformal radii replaced by harmonic ones. The main tool used in the proof is the technique of generalized reduced modules. We also apply the method of extremal metrics and dissymmetrization of families of curves.