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BOUNDARY ACCESSIBILITY OF A DOMAIN QUASICONFORMALLY EQUIVALENT TO A BALL

Published online by Cambridge University Press:  23 December 2003

OLLI MARTIO  and
RAIMO NÄKKI
OLLI MARTIO
Affiliation:
Department of Mathematics, P. O. Box 4 FIN-00014, University of Helsinki, Finland
RAIMO NÄKKI
Affiliation:
Department of Mathematics and Statistics, P. O. Box 35, FIN-40014 University of Jyväskylä, Finland
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Abstract

A boundary point of a domain $D$ in $\Bbb{R}^n$ is said to be broadly accessible if it ‘almost lies’ on the boundary of a round ball contained in $D$. If $f$ is a quasiconformal mapping of the unit ball $B^n$ onto $D$, then it is shown that broadly accessible boundary points on $\partial D$ correspond under $f$ to a set of full measure on $\partial B^n$.This research was carried out while R. Näkki was visiting The University of Texas at Austin in 1985–86.

Keywords

30C65
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 1 , January 2004 , pp. 115 - 118
Copyright
© The London Mathematical Society 2004

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