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On Belinskii conformality in countable sets of points
Author(s):
Vladimir
I.
Ryazanov;
Matti
K.
Vuorinen
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3049-3056.
MSC (1991):
Primary 30C62;
Secondary 30G15
Posted:
April 9, 2001
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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:
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
Posted:
April 9, 2001
Dedicated:
Dedicated to Professor P.P. Belinskii
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
2001,
American Mathematical Society
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