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Homeomorphisms of finite distortion: discrete length of radial images

Published online by Cambridge University Press:  01 January 2008

PEKKA KOSKELA  and
TOMI NIEMINEN
PEKKA KOSKELA
Affiliation:
University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35, FIN-40014 Jyväskylä, Finland. e-mail: pkoskela@maths.jyu.fi, tominiem@maths.jyu.fi
TOMI NIEMINEN
Affiliation:
University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35, FIN-40014 Jyväskylä, Finland. e-mail: pkoskela@maths.jyu.fi, tominiem@maths.jyu.fi
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Abstract

We study homeomorphisms of finite exponentially integrable distortion of the unit ball Bn onto a domain Ω of finite volume. We show that under such a mapping the images of almost all radii (in terms of a gauge dimension) have finite discrete length. We also show that our dimension estimate is essentially sharp.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 1 , January 2008 , pp. 197 - 205
Copyright
Copyright © Cambridge Philosophical Society 2008

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