Keywords

• complex analysis
• univalent function
• holomorphic function
• conformal mapping

Abstract. The talk is devoted to a rather old topic in Complex Analysis - representation of univalent (= holomorphic and injective) functions of a complex variable via integrals of Loewner’s differential equation and its analogues, with applications to problems in conformal mapping. After introducing Loewner’s classical method and important results obtained with its help, the main focus will be made on recent developments in the topic for the last 20 years, including applications to univalent functions with quasiconformal extensions and conformal mappings with prescribed boundary fixed points.