On Belinskii conformality in countable sets of points
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- by Vladimir I. Ryazanov and Matti K. Vuorinen PDF
- Proc. Amer. Math. Soc. 129 (2001), 3049-3056 Request permission
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.References
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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
- MR Author ID: 179630
- Email: vuorinen@csc.fi
- Received by editor(s): October 26, 1999
- Received by editor(s) in revised form: March 9, 2000
- Published electronically: April 9, 2001
- Communicated by: Albert Baernstein II
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3049-3056
- MSC (1991): Primary 30C62; Secondary 30G15
- DOI: https://doi.org/10.1090/S0002-9939-01-05932-9
- MathSciNet review: 1840111
Dedicated: Dedicated to Professor P.P. Belinskii