Moduli in Modern Mapping Theory

Olli Martio

ISBN 10: 1441927557 / ISBN 13: 9781441927552

Published by Springer New York, Springer US, 2010

About this Item

Druck auf Anfrage Neuware - Printed after ordering - The purpose of this book is to present modern developments and applications of the techniques of modulus or extremal length of path families in the study of m- n pings in R , n 2, and in metric spaces. The modulus method was initiated by Lars Ahlfors and Arne Beurling to study conformal mappings. Later this method was extended and enhanced by several other authors. The techniques are geom- ric and have turned out to be an indispensable tool in the study of quasiconformal and quasiregular mappings as well as their generalizations. The book is based on rather recent research papers and extends the modulus method beyond the classical applications of the modulus techniques presented in many monographs. Helsinki O. Martio Donetsk V. Ryazanov Haifa U. Srebro Holon E. Yakubov 2007 Contents 1 Introduction and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Moduli and Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. 2 Moduli in Metric Spaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. 3 Conformal Modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2. 4 Geometric De nition for Quasiconformality . . . . . . . . . . . . . . . . . . . . 13 2. 5 Modulus Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2. 6 Upper Gradients and ACC Functions . . . . . . . . . . . . . . . . . . . . . . . . . 17 p n 2. 7 ACC Functions in R and Capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 p 2. 8 Linear Dilatation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2. 9 Analytic De nition for Quasiconformality. . . . . . . . . . . . . . . . . . . . . . 31 n 2. 10 R as a Loewner Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2. 11 Quasisymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3 Moduli and Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. 2 QED Exceptional Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3. 3 QED Domains and Their Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3. 4 UniformandQuasicircleDomains . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Seller Inventory # 9781441927552

Bibliographic Details

• Title: Moduli in Modern Mapping Theory
• Publisher: Springer New York, Springer US
• Publication Date: 2010
• Language: English
• ISBN 10: 1441927557
• ISBN 13: 9781441927552
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 21D millimeters 235 millimeters width by 155 millimeters height by 21 millimeters depth
• Weight: 575 grams

About this title

Synopsis

Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

From the Back Cover

The purpose of this book is to present a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. The modulus method was initiated by Arne Beurling and Lars Ahlfors to study conformal mappings, and later this method was extended and enhanced by several others. The techniques are geometric and they have turned out to be an indispensable tool in the study of quasiconformal and quasiregular mappings as well as their generalizations. The book is based on recent research papers and extends the modulus method beyond the classical applications of the modulus techniques presented in many monographs.