Quasiconformal Maps and Teichmuller Theory

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 Teichmüller theory.

Table of Contents

1 The Grotzsch 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 Teichmuller spaces

8 Extremal quasiconformal mappings

9 Unique extremality

10 Isomorphisms of Teichmuller space

11 Local rigidity of Teichmuller spaces

About the Author

Vladimir Marković is a Professor of Mathematics at University of Oxford. He was previously the John D. MacArthur Professor at the California Institute of Technology and Sadleirian Professor of Pure Mathematics at the University of Cambridge.