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PATHWISE CONNECTIVITY OF A CONFORMAL BOUNDARY

Published online by Cambridge University Press:  13 August 2003

PEKKA KOSKELA  and
TIMO TOSSAVAINEN
PEKKA KOSKELA
Affiliation:
Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40351 Jyväskylä, Finlandpkoskela@maths.jyu.fi
TIMO TOSSAVAINEN
Affiliation:
Department of Teacher Education, University of Joensuu, P.O. Box 55, 57101 Savonlinna, Finlandtimo.tossavainen@joensuu.fi
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Abstract

This paper demonstrates that, in dimensions $n\ge 3$, the metric boundary of a conformal deformation of the unit ball is pathwise connected, and even of bounded turning, provided that the conformal scaling factor satisfies a Harnack inequality and the volume growth of the deformed space is at most euclidean.

Keywords

30C65
Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 5 , September 2003 , pp. 645 - 650
Copyright
© The London Mathematical Society 2003

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