Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings

Inbunden, Engelska, 2017

Del i serien Mathematical Surveys and Monographs

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2017-07-30
Mått:178 x 254 x undefined mm
Vikt:935 g
Format:Inbunden
Språk:Engelska
Serie:Mathematical Surveys and Monographs
Antal sidor:430
Förlag:American Mathematical Society
ISBN:9780821843604

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Frederick W. Gehring, and Gaven J. Martin, Massey University, Auckland, New Zealand.Bruce P. Palka, National Science Foundation, Arlington, VA.

Recensioner i media

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

Innehållsförteckning

IntroductionTopology and analysisConformal mappings in Euclidean spaceThe moduli of curve familiesRings and condensersQuasiconformal mappingsMapping problemsThe Tukia-Vaisala extension theoremThe Mostow rigidity theorem and discrete Mobius groupsBasic notationBibliographyIndex