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On quasiplanes in Euclidean spaces


Authors: O. Martio, V. M. Miklyukov and M. Vuorinen
Journal: Proc. Amer. Math. Soc. 135 (2007), 2433-2442
MSC (2000): Primary 30C62, 30C65
DOI: https://doi.org/10.1090/S0002-9939-07-09117-4
Published electronically: April 5, 2007
MathSciNet review: 2302564
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Abstract: A variational inequality for the images of $k$-dimensional hyperplanes under quasiconformal maps of the $n$-dimensional Euclidean space is proved when $1\le k\le n-2.$


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Additional Information

O. Martio
Affiliation: Department of Mathematics and Statistics, University of Helsinki, 00014 Helsinki, Finland
MR Author ID: 120710
Email: martio@cc.helsinki.fi

V. M. Miklyukov
Affiliation: Mathematics Department, Volgograd State University, 2 Prodolnaya 30, Volgograd 400062, Russia
Email: miklyuk@hotmail.com

M. Vuorinen
Affiliation: Department of Mathematics, University of Turku, 20014 Turku, Finland
MR Author ID: 179630
Email: vuorinen@utu.fi

Keywords: Quasiconformal mapping, quasiconformal curve, quasicircle, uniform domain, quasidisk, quasiplane.
Received by editor(s): April 27, 2004
Received by editor(s) in revised form: July 18, 2005, and November 6, 2005
Published electronically: April 5, 2007
Communicated by: Andreas Seeger
Article copyright: © Copyright 2007 American Mathematical Society