Zabolotnyi Y. Extremal problems 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. In such a way, we generalize and improve a number of results obtained in the papers of well-known experts in geometric function theory of the complex variable. We obtained a partial solution of the following Dubinin problem: to determine the maximum of product of the inner radii of n non-overlapping domains, which contain some points on the unit circle, and the some positive power of the inner radius of a domain, which contains the origin. By introducing this concept we able to transfer the results known in the case of the complex plane, on n-dimensional complex space.