Quasiconformal Maps and Teichmüller Theory

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 Grotzch 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 ; References ; Index

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