Lectures on Quasiconformal Mappings: Second Edition
About this Title
Lars V. Ahlfors
Publication: University Lecture Series
Publication Year 2006: Volume 38
ISBNs: 978-0-8218-3644-6 (print); 978-1-4704-1832-8 (online)
MathSciNet review: MR2241787
MSC: Primary 30-01; Secondary 30-02, 30C62, 30D05, 30F45, 30F60
Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmüller spaces, including the Bers embedding and the Teichmüller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmüller spaces from these lecture notes.
This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmüller spaces and provides many references to the vast literature on Teichmüller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.
Graduate students and research mathematicians interested in complex analysis.
Table of Contents
- Chapter I. Differentiable quasiconformal mappings
- Chapter II. The general definition
- Chapter III. Extremal geometric properties
- Chapter IV. Boundary correspondence
- Chapter V. The mapping theorem
- Chapter VI. Teichmüller spaces
- Editors’ notes
- Clifford J. Earle and Irwin Kra – A supplement to Ahlfors’s lectures
- Mitsuhiro Shishikura – Complex dynamics and quasiconformal mappings
- John H. Hubbard – Hyperbolic structures on three-manifolds that fiber over the circle