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About the Gradient of the Conformal Radius

  • A. N. AkhmetovaEmail author
  • L. A. Aksentyev
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 221)

Abstract

Let D be a simply connected domain in \(\overline{\mathbb{C}}\) and R(D, z) the conformal radius of D at the point \(z \in D/ \{\infty\}\)We discuss the function \(\nabla R(D,z)\) In particular, we prove that \(\nabla R(D,z)\) is a quasi-conformal mapping of D for different types of domains.

Keywords

Conformal radius hyperbolic radius gradient of the conformal radius quasi-conformal mapping 

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References

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    F.G. Avkhadiev, K.-J. Wirths, The conformal radius as a function and its gradient image. Israel J. of Mathematics 145 (2005), 349–374.MathSciNetzbMATHCrossRefGoogle Scholar
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    L.A. Aksentyev, A.N. Akhmetova, On mappings related to the gradient of the conformal radius. Izv. VUZov. Mathematics 6 (2009), 60–64 (the short message).Google Scholar
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    L.A. Aksentyev, A.N. Akhmetova, On mappings related to the gradient of the conformal radius. Mathematical Notes 1 (2010), 3–12.CrossRefGoogle Scholar
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    G.M. Goluzin, Geometric theory of the function of complex variables. Nauka, 1966.Google Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Kazan State Technical UniversityKazanRussia
  2. 2.Kazan (Volga region), Federal UniversityKazanRussia

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