Developments in Mathematics

The Beltrami Equation

A Geometric Approach

Authors: Gutlyanskii, V., Ryazanov, V., Srebro, U., Yakubov, E.

  • Features a unified  geometric approach based on the modulus method that is effectively applied to solving the Beltrami equation problems  
  • Presents recent developments in the theory of Beltrami equations, especially on degenerate and alternating Beltrami equations  
  • Discusses new concepts refining the analysis of problems related to the Beltrami equation, as well as applications of new research tools​
  • Authors are well-known specialists in geometric function theory and elliptic differential equations
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Hardcover $179.00
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  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
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  • ISBN 978-1-4899-9302-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this book

This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis,  meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics,  potential theory, electrostatics, magnetostatics,  hydrodynamics and magneto-hydrodynamics.

The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions  to the Beltrami equations that turned out to be not only sufficient but also necessary.

The most important feature of this book concerns the unified  geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.​

Table of contents (10 chapters)

  • Introduction

    Gutlyanskii, Vladimir (et al.)

    Pages 1-4

  • Preliminaries

    Gutlyanskii, Vladimir (et al.)

    Pages 5-45

  • The Classical Beltrami Equation ||µ||∞<1

    Gutlyanskii, Vladimir (et al.)

    Pages 47-53

  • The Degenerate Case

    Gutlyanskii, Vladimir (et al.)

    Pages 55-76

  • BMO- and FMO-Quasiconformal Mappings

    Gutlyanskii, Vladimir (et al.)

    Pages 77-95

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-1-4614-3191-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-1-4614-3190-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-1-4899-9302-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Beltrami Equation
Book Subtitle
A Geometric Approach
Authors
Series Title
Developments in Mathematics
Series Volume
26
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-3191-6
DOI
10.1007/978-1-4614-3191-6
Hardcover ISBN
978-1-4614-3190-9
Softcover ISBN
978-1-4899-9302-1
Series ISSN
1389-2177
Edition Number
1
Number of Pages
XIV, 302
Topics