Based on a series of graduate lectures given by Vladimir Markovic at the University of Warwick in spring 2003, this book is accessible to those with a grounding in complex analysis looking for an introduction to the theory of quasiconformal maps and Teichm ller theory. Assuming some familiarity with Riemann surfaces and hyperbolic geometry, topics covered include the Gr tzch argument, analytical properties of quasiconformal maps, the Beltrami differential equation, holomorphic motions and Teichm ller spaces. Where proofs are omitted, references to where they may be found are always given, and the text is clearly illustrated throughout with diagrams, examples, and exercises for the reader.

Vladimir Markovic is a Professor in the Mathematics department of the University of Warwick. In 2004 he was awarded the Philip Leverhulme prize and the Whitehead prize for his work on infinite-dimensional Teichmüller spaces.; Alastair Fletcher is a final year PhD student under the supervision of Professor Markovic at the University of Warwick. His research interests lie in the field of complex analysis and Teichmüller theory.

• Preface


• 1: The Grötzch argument


• 2: Geometric definition of quasiconformal maps


• 3: Analytic properties of quasiconformal maps


• 4: Quasi-isometries and quasisymmetric maps


• 5: The Beltrami differential equation


• 6: Holomorphic motions and applications


• 7: Teichmüller spaces


• 8: Extremal quasiconformal mappings


• 9: Unique extremality


• 10: Isomorphisms of Teichmüller space


• 11: Local rigidity of Teichmüller spaces


• References


• Index