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 ...
- ISBN10 0387856684
- ISBN13 9780387856681
- Publish Date 21 March 2011 (first published 2 December 2008)
- Publish Status Withdrawn
- Out of Print 18 October 2014
- Publish Country US
- Imprint Springer
- Format Paperback (US Trade)
- Pages 380
- Language English