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The Classical Beltrami Equation ||µ||<1

  • Vladimir Gutlyanskii
  • Vladimir Ryazanov
  • Uri Srebro
  • Eduard Yakubov
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 26)

Abstract

Consider the Beltrami equation (B) in Sect. 1.1 with ||µ||<1, and let f : D → ℂ be its homeomorphic solution. Since |µ| < 1 a.e., f is sense preserving, and since ||µ||<1, f is a quasiconformal mapping.

Keywords

Riemann Surface Conformal Mapping Quasiconformal Mapping Conformal Structure Beltrami Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vladimir Gutlyanskii
    • 1
  • Vladimir Ryazanov
    • 2
  • Uri Srebro
    • 3
  • Eduard Yakubov
    • 4
  1. 1.Department of the Partial Differential Equations Institute of Applied Mathematics and MechanicsNational Academy of Sciences of UkraineDonetskUkraine
  2. 2.Department of the Function Theory Institute of Applied Mathematics and MechanicsNational Academy of Sciences of UkraineDonetskUkraine
  3. 3.Faculty of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael
  4. 4.Faculty of SciencesH.I.T. – Holon Institute of TechnologyHolonIsrael

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