Moduli in Modern Mapping Theory

• Main Authors: Martio, Olli. (Author), Ryazanov, Vladimir. (Author), Srebro, Uri. (Author), Yakubov, Eduard. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Global analysis (Mathematics).; Functional analysis.; Analysis.; Functional Analysis.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-85588-2

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...

Table of Contents:

• Introduction and notation
• Moduli and capacity
• Moduli and domains
• Q-Homeomorphisms
• Q-Homeomorphisms with Q in BMO
• More General Q-Homeomorphisms
• Ring Q-Homeomorphisms
• Mappings With Finite Length Distortions (FLD)
• Lower Q-Homeomorphisms
• Mappings With Finite Area Distortions (FAD)
• On Ring Solutions of the Beltrami Equation
• Homeomorphisms with Finite Means Dilatations
• On the Mapping Theory in Metric Spaces
• Moduli Theory
• BMO Functions by John-Nirenberg
• References
• Index.