Softcover ISBN:  9780821836446 
Product Code:  ULECT/38 
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Electronic ISBN:  9781470418328 
Product Code:  ULECT/38.E 
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Book DetailsUniversity Lecture SeriesVolume: 38; 2006; 162 ppMSC: Primary 30;
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 selfcontained 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 3manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.ReadershipGraduate students and research mathematicians interested in complex analysis.

Table of Contents

The Ahlfors lectures [ MR MR2241787 ]

Acknowledgments

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

The additional chapters [ MR MR2241787 ]

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 threemanifolds that fiber over the circle


Additional Material

Reviews

The lectures and supplements constitute a very efficient way of learning some complicated theories with numerous applications.
EMS Newsletter 
Most library copies of the first edition are now very wellthumbed from use by generations of mathematicians, so this second edition is very welcome. ... The second edition is made much more valuable by the addition of three new chapters by leading authorities in fields where quasiconformal mappings have proved especially fruitful.
Mathematical Reviews


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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 selfcontained 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 3manifolds. 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.

The Ahlfors lectures [ MR MR2241787 ]

Acknowledgments

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

The additional chapters [ MR MR2241787 ]

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 threemanifolds that fiber over the circle

The lectures and supplements constitute a very efficient way of learning some complicated theories with numerous applications.
EMS Newsletter 
Most library copies of the first edition are now very wellthumbed from use by generations of mathematicians, so this second edition is very welcome. ... The second edition is made much more valuable by the addition of three new chapters by leading authorities in fields where quasiconformal mappings have proved especially fruitful.
Mathematical Reviews