Quasiconformal Maps and Teichmüller Theory
This text is based on a series of graduate lectures given by V. Markovic at the University of Warwick. The book is intended as an introduction to quasiconformal mappings in dimension 2 and Teichmüller theory. The reader is assumed to have a background in complex analysis and to be familiar with Riemann surfaces and hyperbolic geometry. The book starts with analytic and geometric definitions of quasiconformal mappings and continues with a study of their basic analytical properties. The connection with quasisymmetric maps and the Beltrami equation is explained in the following chapters, before a presentation of the definitions and basic properties of holomorphic motions and Teichmüller spaces. Extremal quasiconformal mappings are studied together with conditions that guarantee the unique extremality of a mapping. The book is well-written and illustrated with a number of examples. Some proofs are omitted but references to other sources are always given.