Overview
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 ...
Full Product Details
Author: Olli Martio ,
Vladimir Ryazanov ,
Uri Srebro ,
Eduard Yakubov
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 2009 ed.
Dimensions:
Width: 15.50cm
, Height: 2.20cm
, Length: 23.50cm
Weight: 0.735kg
ISBN: 9780387855868
ISBN 10: 0387855866
Pages: 367
Publication Date: 02 December 2008
Audience:
Professional and scholarly
,
College/higher education
,
Professional & Vocational
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
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)
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)
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)
