October 23, 2011 - 20:52 — Anonymous

Publisher:

Oxford University Press, Oxford: Oxford Graduate Texts in Mathematics 11

Year:

2006

ISBN:

0-19-856926-2

Price (tentative):

GBP 45

MSC main category:

30 Functions of a complex variable

Review:

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.

Reviewer:

hencl