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Hardcover ISBN:  9780821890868 
Product Code:  SURV/184 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9780821894095 
Product Code:  SURV/184.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821890868 
eBook ISBN:  9780821894095 
Product Code:  SURV/184.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 184; 2012; 171 ppMSC: Primary 30
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 twosided 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 twentynine 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.
ReadershipGraduate students and research mathematicians interested in geometric function theory.

Table of Contents

Part 1. Properties of quasidisks

1. Preliminaries

2. Geometric properties

3. Conformal invariants

4. Injectivity criteria

5. Criteria for extension

6. Twosided criteria

7. Miscellaneous properties

Some proofs of these properties

8. First series of implications

9. Second series of implications

10. Third series of implications

11. Fourth series of implications


Additional Material

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


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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 twosided 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 twentynine 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.
Graduate students and research mathematicians interested in geometric function theory.

Part 1. Properties of quasidisks

1. Preliminaries

2. Geometric properties

3. Conformal invariants

4. Injectivity criteria

5. Criteria for extension

6. Twosided criteria

7. Miscellaneous properties

Some proofs of these properties

8. First series of implications

9. Second series of implications

10. Third series of implications

11. Fourth series of implications

...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