Symmetrization of condensers and geometrical properties of multivalent functions

In the talk we will give a brief survey of new distortion theorems for holomorphic functions, in which critical values of functions under consideration and the character of the respective covering of a given sets are taken into account. All results are obtained using one general method based on the concept of a circular symmetrization of condensers on Riemann surfaces. One theorem about change of a condenser capacity under symmetrization will be formulated and some its applications to multivalent functions of certain classes will be considered.