Overview
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.
Full Product Details
Author: Frederick W. Gehring ,
Gaven J. Martin ,
Bruce P. Palka
Publisher: American Mathematical Society
Imprint: American Mathematical Society
Weight: 0.935kg
ISBN: 9780821843604
ISBN 10: 0821843605
Pages: 430
Publication Date: 30 July 2017
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
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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"
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
Author Information
Frederick W. Gehring, and Gaven J. Martin, Massey University, Auckland, New Zealand. Bruce P. Palka, National Science Foundation, Arlington, VA.
