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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Belinskii conformality in countable sets of points


Authors: Vladimir I. Ryazanov and Matti K. Vuorinen
Journal: Proc. Amer. Math. Soc. 129 (2001), 3049-3056
MSC (1991): Primary 30C62; Secondary 30G15
Published electronically: April 9, 2001
MathSciNet review: 1840111
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Abstract:

The local behavior of plane quasiconformal mappings is investigated. In particular, generalizing the well-known Reich-Walczak problem, we study the possibility for a quasiconformal mapping to be conformal in the sense of Belinskii at a prescribed point or in a prescribed set of points when the modulus of the complex dilatation is a fixed measurable function. The notion of the Belinskii conformality is related to the conception of asymptotical rotations by Brakalova and Jenkins.


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Additional Information

Vladimir I. Ryazanov
Affiliation: Institute of Applied Mathematics and Mechanics, NAS of Ukraine, ul. Roze Luxemburg 74, 340114, Donetsk, Ukraine
Address at time of publication: Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), FIN–00014 University of Helsinki, Finland
Email: ryaz@iamm.ac.donetsk.ua, ryazanov@www.math.helsinki.fi

Matti K. Vuorinen
Affiliation: Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), FIN–00014 University of Helsinki, Finland
Email: vuorinen@csc.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05932-9
PII: S 0002-9939(01)05932-9
Keywords: Quasiconformal mappings, local behavior, conformality, asymptotical rotations
Received by editor(s): October 26, 1999
Received by editor(s) in revised form: March 9, 2000
Published electronically: April 9, 2001
Dedicated: Dedicated to Professor P.P. Belinskii
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 American Mathematical Society