Moduli in modern mapping theory
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Bibliographic Information
Moduli in modern mapping theory
（Springer monographs in mathematics）
Springer, c2009
Available at / 27 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Other authors: Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
Includes bibliographical references (p. [351]-363) and index
HTTP:URL=http://dx.doi.org/10.1007/978-0-387-85588-2
Description and Table of Contents
Description
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 ...
Table of Contents
and Notation.- Moduli and Capacity.- Moduli and Domains.- Q-Homeomorphisms with Q? Lloc1.- Q-homeomorphisms with Q in BMO.- More General Q-Homeomorphisms.- Ring Q-Homeomorphisms.- Mappings with Finite Length Distortion (FLD).- Lower Q-Homeomorphisms.- Mappings with Finite Area Distortion.- On Ring Solutions of the Beltrami Equation.- Homeomorphisms with Finite Mean Dilatations.- On Mapping Theory in Metric Spaces.
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