Denega I. Separating transformation in geometric function theory of complex variable

This work is devoted to one of the classic partitions of geometric function theory of complex variable, namely, extremal problems on non-overlapping domains. An approach based on the methods of separating transformation, quadratic differentials, "control" functionals is proposed. By this approach we generalize and improve a number of known results obtained in the works of famous specialists geometric function theory of complex variable G.V. Kuzmina, V.N. Dubinin, L.V. Kovalev, A.K. Bakhtin. Moreover, statement of one open problem of V.N. Dubinin are generalized. A partial solution of this generalized problem of V.N. Dubinin is obtained. It summarizes almost all known results on this problem. А notion of inner radius is generalized on the case of n-dimensional complex space, namely, we introduce a concept of generalized inner radius. By introducing this concept we able to transfer the results known in the case of the complex plane, on n-dimensional complex space.