**Mathematical Surveys and Monographs**

Volume: 184;
2012;
171 pp;
Hardcover

MSC: Primary 30;

Print ISBN: 978-0-8218-9086-8

Product Code: SURV/184

List Price: $74.00

Individual Member Price: $59.20

**Electronic ISBN: 978-0-8218-9409-5
Product Code: SURV/184.E**

List Price: $74.00

Individual Member Price: $59.20

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#### Supplemental Materials

# The Ubiquitous Quasidisk

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*Frederick W. Gehring; Kari Hag*

This book focuses on gathering the numerous properties and many different connections with various topics in geometric function theory that quasidisks possess. A quasidisk is the image of a disk under a quasiconformal mapping of the Riemann sphere. In 1981 Frederick W. Gehring gave a short course of six lectures on this topic in Montreal and his lecture notes “Characteristic Properties of Quasidisks” were published by the University Press of the University of Montreal. The notes became quite popular and within the next decade the number of characterizing properties of quasidisks and their ramifications increased tremendously. In the late 1990s Gehring and Hag decided to write an expanded version of the Montreal notes. At three times the size of the original notes, it turned into much more than just an extended version. New topics include two-sided criteria. The text will be a valuable resource for current and future researchers in various branches of analysis and geometry, and with its clear and elegant exposition the book can also serve as a text for a graduate course on selected topics in function theory.

Frederick W. Gehring (1925–2012) was a leading figure in the theory of quasiconformal mappings for over fifty years. He received numerous awards and shared his passion for mathematics generously by mentoring twenty-nine Ph.D. students and more than forty postdoctoral fellows.

Kari Hag received her Ph.D. under Gehring's direction in 1972 and worked with him on the present text for more than a decade.

#### Table of Contents

# Table of Contents

## The Ubiquitous Quasidisk

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Part I. Properties of quasidisks 114 free
- Preliminaries 316
- Geometric properties 1932
- Conformal invariants 3346
- Injectivity criteria 5972
- Criteria for extension 6982
- Two-sided criteria 7790
- Miscellaneous properties 87100
- Part II. Some proofs of these properties 97110
- First series of implications 99112
- Second series of implications 117130
- Third series of implications 137150
- Fourth series of implications 149162
- Bibliography 163176
- Index 169182 free
- Back Cover Back Cover1185

#### Readership

Graduate students and research mathematicians interested in geometric function theory.

#### Reviews

...This text on quasidisks provides a cross section of the plane quasiconformal theory and demonstrates the many ways in which these mappings are related to analysis, topology, geometry and other parts of mathematics. The exposition is very clear and the text is richly illustrated with carefully drawn pictures. This book would be an excellent choice for a first book on plane quasiconformal maps for a graduate student. It is also a valuable source of inspiration for researchers of complex analysis, because the material covers many topics of current interest. It is my guess that this book will be an instant classic in its field.

-- Matti Vuorinen (Turku), Zentralblatt MATH