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Lectures on Quasiconformal Mappings: Second Edition

with additional chapters by C. J. Earle and I. Kra, M. Shishikura, J. H. Hubbard
Available Formats:
Softcover ISBN: 978-0-8218-3644-6
Product Code: ULECT/38
List Price: $41.00 MAA Member Price:$36.90
AMS Member Price: $32.80 Electronic ISBN: 978-1-4704-1832-8 Product Code: ULECT/38.E List Price:$38.00
MAA Member Price: $34.20 AMS Member Price:$30.40
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List Price: $61.50 MAA Member Price:$55.35
AMS Member Price: $49.20 Click above image for expanded view Lectures on Quasiconformal Mappings: Second Edition with additional chapters by C. J. Earle and I. Kra, M. Shishikura, J. H. Hubbard Available Formats:  Softcover ISBN: 978-0-8218-3644-6 Product Code: ULECT/38  List Price:$41.00 MAA Member Price: $36.90 AMS Member Price:$32.80
 Electronic ISBN: 978-1-4704-1832-8 Product Code: ULECT/38.E
 List Price: $38.00 MAA Member Price:$34.20 AMS Member Price: $30.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$61.50 MAA Member Price: $55.35 AMS Member Price:$49.20
• Book Details

University Lecture Series
Volume: 382006; 162 pp
MSC: 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 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.

• 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 three-manifolds that fiber over the circle

• Reviews

• The lectures and supplements constitute a very efficient way of learning some complicated theories with numerous applications.

• Most library copies of the first edition are now very well-thumbed 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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Volume: 382006; 162 pp
MSC: 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 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.

• 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 three-manifolds that fiber over the circle
• The lectures and supplements constitute a very efficient way of learning some complicated theories with numerous applications.