Some applications of extremal decompositions in the geometric function theory

The applications of the extremal decompositions of the domains and condensers in the geometric function theory are considered. We prove new theorems for the families of meromorphic functions without common values, the multipoint distortion theorems and the estimates of the coefficients for univalent functions. Also, we get some new inequalities for polynomials. All results are obtained by the unified method using the suitable properties of the extremal decompositions. Previously, these properties were established by capacity approach and symmetrization.