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.
Author(s): Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov (auth.)
Series: Springer Monographs in Mathematics
Edition: 1
Publisher: Springer-Verlag New York
Year: 2009
Language: English
Pages: 367
Tags: Analysis; Functional Analysis
Front Matter....Pages I-XII
Introduction and Notation....Pages 1-6
Moduli and Capacity....Pages 7-46
Moduli and Domains....Pages 47-79
Q -Homeomorphisms with Q ∈ L loc 1 ....Pages 81-92
Q -homeomorphisms with Q in BMO....Pages 93-102
More General Q -Homeomorphisms....Pages 103-129
Ring Q -Homeomorphisms....Pages 131-144
Mappings with Finite Length Distortion (FLD)....Pages 145-173
Lower Q -Homeomorphisms....Pages 175-191
Mappings with Finite Area Distortion....Pages 193-204
On Ring Solutions of the Beltrami Equation....Pages 205-235
Homeomorphisms with Finite Mean Dilatations....Pages 237-255
On Mapping Theory in Metric Spaces....Pages 257-289
Back Matter....Pages 291-367
