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Moduli in Modern Mapping Theory (Hardcover, 2009 ed.)
Loot Price: R3,878
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Moduli in Modern Mapping Theory (Hardcover, 2009 ed.)
Series: Springer Monographs in Mathematics
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Total price: R3,898
Discovery Miles: 38 980
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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 . . . . . . . . . . . . . . . . . . .
. . . . . . . . .
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