**University Lecture Series**

Volume: 38;
2006;
162 pp;
Softcover

MSC: Primary 30;

Print ISBN: 978-0-8218-3644-6

Product Code: ULECT/38

List Price: $38.00

Individual Member Price: $30.40

**Electronic ISBN: 978-1-4704-1832-8
Product Code: ULECT/38.E**

List Price: $38.00

Individual Member Price: $30.40

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#### Supplemental Materials

# Lectures on Quasiconformal Mappings: Second Edition

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*Lars V. Ahlfors*

with additional chapters by C. J. Earle and I. Kra, M. Shishikura, J. H. Hubbard

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.

#### Table of Contents

# Table of Contents

## Lectures on Quasiconformal Mappings: Second Edition

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Part I. The Ahlfors Lectures 110 free
- Acknowledgments 312
- Differentiable quasiconformal mappings 514
- The general definition 1524
- Extremal geometric properties 2332
- Boundary correspondence 3948
- The mapping theorem 5160
- Teichmüller spaces 6776
- Editors’ notes 8392
- Part II. The Additional Chapters 8594
- A supplement to Ahlfors’s lectures 8796
- Complex dynamics and quasiconformal mappings 119128
- Hyperbolic structures on three-manifolds that fiber over the circle 143152
- Back Cover Back Cover1178

#### Readership

Graduate students and research mathematicians interested in complex analysis.

#### 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 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