Hardcover ISBN:  9780821843604 
Product Code:  SURV/216 
List Price:  $116.00 
MAA Member Price:  $104.40 
AMS Member Price:  $92.80 
Electronic ISBN:  9781470440466 
Product Code:  SURV/216.E 
List Price:  $116.00 
MAA Member Price:  $104.40 
AMS Member Price:  $92.80 

Book DetailsMathematical Surveys and MonographsVolume: 216; 2017; 430 ppMSC: Primary 30;
This book offers a modern, uptodate 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 higherdimensional 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.ReadershipGraduate students and researchers interested in mapping theory.

Table of Contents

Chapters

Introduction

Topology and analysis

Conformal mappings in Euclidean space

The moduli of curve families

Rings and condensers

Quasiconformal mappings

Mapping problems

The TukiaVäisälä extension theorem

The Mostow rigidity theorem and discrete Möbius groups


Additional Material

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


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This book offers a modern, uptodate 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 higherdimensional 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 TukiaVäisälä 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