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An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings

Gaven J. Martin Massey University, Auckland, New Zealand
Bruce P. Palka National Science Foundation, Arlington, VA
Available Formats:
Hardcover ISBN: 978-0-8218-4360-4
Product Code: SURV/216
List Price: $116.00 MAA Member Price:$104.40
AMS Member Price: $92.80 Electronic ISBN: 978-1-4704-4046-6 Product Code: SURV/216.E List Price:$116.00
MAA Member Price: $104.40 AMS Member Price:$92.80
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List Price: $174.00 MAA Member Price:$156.60
AMS Member Price: $139.20 Click above image for expanded view An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings Gaven J. Martin Massey University, Auckland, New Zealand Bruce P. Palka National Science Foundation, Arlington, VA Available Formats:  Hardcover ISBN: 978-0-8218-4360-4 Product Code: SURV/216  List Price:$116.00 MAA Member Price: $104.40 AMS Member Price:$92.80
 Electronic ISBN: 978-1-4704-4046-6 Product Code: SURV/216.E
 List Price: $116.00 MAA Member Price:$104.40 AMS Member Price: $92.80 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:$174.00 MAA Member Price: $156.60 AMS Member Price:$139.20
• Book Details

Mathematical Surveys and Monographs
Volume: 2162017; 430 pp
MSC: Primary 30;

This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background.

This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.

Graduate students and researchers interested in mapping theory.

• Chapters
• Introduction
• Topology and analysis
• Conformal mappings in Euclidean space
• The moduli of curve families
• Rings and condensers
• Quasiconformal mappings
• Mapping problems
• The Tukia-Väisälä extension theorem
• The Mostow rigidity theorem and discrete Möbius groups

• Reviews

• GMP are to be commended for writing their monograph with a remarkable attention to detail...Readers keen to engage with the material could easily attempt to prove any of the results as exercises. I am confident that this book will very soon become a standard basic reference.

Tushar Das, MAA Reviews
• The content of this book is precisely articulated while an inviting and, at times, conversational tone is maintained. This combination makes for a pleasant reading experience. The presentation of content is clearly organized and follows a natural progression of ideas.

David Matthew Freeman, Mathematical Reviews
• [T]he book takes a wider approach to the modern theory of quasiconformal mappings and its applications than what is usual in more specialized books.

Olli Martio, Zentralblatt MATH
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2162017; 430 pp
MSC: Primary 30;

This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background.

This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.

Graduate students and researchers interested in mapping theory.

• Chapters
• Introduction
• Topology and analysis
• Conformal mappings in Euclidean space
• The moduli of curve families
• Rings and condensers
• Quasiconformal mappings
• Mapping problems
• The Tukia-Väisälä extension theorem
• The Mostow rigidity theorem and discrete Möbius groups
• GMP are to be commended for writing their monograph with a remarkable attention to detail...Readers keen to engage with the material could easily attempt to prove any of the results as exercises. I am confident that this book will very soon become a standard basic reference.

Tushar Das, MAA Reviews
• The content of this book is precisely articulated while an inviting and, at times, conversational tone is maintained. This combination makes for a pleasant reading experience. The presentation of content is clearly organized and follows a natural progression of ideas.

David Matthew Freeman, Mathematical Reviews
• [T]he book takes a wider approach to the modern theory of quasiconformal mappings and its applications than what is usual in more specialized books.

Olli Martio, Zentralblatt MATH
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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