
Moduli in Modern Mapping Theory
Springer (Publisher)
Published on 23. November 2010
Book
Paperback/Softback
XII, 367 pages
978-1-4419-2755-2 (ISBN)
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 ...
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 ...
Reviews / Votes
From the reviews:
"This book is a very welcome addition to the literature on MMT. The topic is fresh and there are a lot of possibilities for new research, as for instance this book itself demonstrates. . best suited to graduate students of mathematical analysis and related topics. . very valuable for all researchers of geometric function theory. Every mathematics graduate library should have a copy of this book." (Matti Vuorinen, Zentralblatt MATH, Vol. 1175, 2010)More details
Series
Edition
1st ed. Softcover of orig. ed. 2009
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
12 s/w Abbildungen
XII, 367 p. 12 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 21 mm
Weight
575 gr
ISBN-13
978-1-4419-2755-2 (9781441927552)
DOI
10.1007/978-0-387-85588-2
Schweitzer Classification
Other editions
Additional editions

Olli Martio | Vladimir Ryazanov | Uri Srebro
Moduli in Modern Mapping Theory
Book
12/2008
Springer
€106.99
Shipment within 5-7 days
Content
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.