On the Asymptotic Behavior of Quasiconformal Mappings in Space

  • V. Ya. Gutlyanskiǐ
  • O. Martio
  • V. I. Ryazanov
  • M. Vuorinen


Conformality at a point of a space quasiconformal mapping is studied without the assumption of differentiability. First, we introduce a notion of asymptotic linearity for general mappings at a prescribed point. Then we prove that the simultaneous asymptotic linearity and analyticity of a mapping f at a point of discreteness imply that f preserves the angles between rays emanating from this point and the moduli of infinitesimal annuli centered at it and thus we strengthen an earlier result of Caraman. Finally, we give sufficient conditions for quasiconformal mappings to be asymptotically linear and analytic in terms of the distortion coefficient and, as a consequence, we generalize the well-known Belinskii weak conformality result to the n-dimensional case.


Quasiconformal Mapping Quasiregular Mapping Asymptotic Linearity Distortion Coefficient Prescribe Point 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • V. Ya. Gutlyanskiǐ
    • 1
    • 2
  • O. Martio
    • 1
    • 2
  • V. I. Ryazanov
    • 1
    • 2
  • M. Vuorinen
    • 1
    • 2
  1. 1.Institute of Applied Mathematics and MechanicsNAS of UkraineDonetskUkraine
  2. 2.Department of MathematicsUniversity of HelsinkiHelsinkiFinland

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