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Moduli in Modern Mapping Theory

  • Book
  • © 2009

Overview

Authors:
  1. Olli Martio

    1. University of Helsinki, Helsinki, Finland

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  2. Vladimir Ryazanov

    1. Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk, Ukraine

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  3. Uri Srebro

    1. Technion - Israel Institute of Technology, Haifa, Israel

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  4. Eduard Yakubov

    1. H.I.T. - Holon Institute of Technology, Holon, Israel

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  • Contains new results from leading researchers in the field
  • Authors have included an extensive bibliography

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction and Notation

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 1-6

  3. Moduli and Capacity

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 7-46

  4. Moduli and Domains

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 47-79

  5. Q-Homeomorphisms with Q∈ Lloc1

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 81-92

  6. Q-homeomorphisms with Q in BMO

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 93-102

  7. More General Q-Homeomorphisms

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 103-129

  8. Ring Q-Homeomorphisms

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 131-144

  9. Mappings with Finite Length Distortion (FLD)

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 145-173

  10. Lower Q-Homeomorphisms

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 175-191

  11. Mappings with Finite Area Distortion

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 193-204

  12. On Ring Solutions of the Beltrami Equation

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 205-235

  13. Homeomorphisms with Finite Mean Dilatations

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 237-255

  14. On Mapping Theory in Metric Spaces

    • Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
    Pages 257-289

  15. Back Matter

    Pages 291-367
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Keywords

About this book

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.

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)

Authors and Affiliations

  • University of Helsinki, Helsinki, Finland

    Olli Martio

  • Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk, Ukraine

    Vladimir Ryazanov

  • Technion - Israel Institute of Technology, Haifa, Israel

    Uri Srebro

  • H.I.T. - Holon Institute of Technology, Holon, Israel

    Eduard Yakubov

Bibliographic Information

  • Book Title: Moduli in Modern Mapping Theory

  • Authors: Olli Martio, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-0-387-85588-2

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag New York 2009

  • Hardcover ISBN: 978-0-387-85586-8Published: 02 December 2008

  • Softcover ISBN: 978-1-4419-2755-2Published: 23 November 2010

  • eBook ISBN: 978-0-387-85588-2Published: 09 November 2008

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XII, 367

  • Number of Illustrations: 12 b/w illustrations

  • Topics: Analysis, Functional Analysis

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