A capacity look at the Schwarzian derivative

In the talk we will give a brief survey of results involving the Schwarzian derivative and depending on the geometry of the image of a domain under a holomorphic map [1]. The author's results obtained previously by using the theory of condenser capacity and symmetrization constitute the core of the talk [2]. Inequalities for univalent and multivalent holomorphic functions are considered both at interior and at boundary points of the domain of definition.