Pathwise Connectivity of a Conformal Boundary |
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| Authors: | Koskela Pekka; Tossavainen Timo |
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| Institution: | Department of Mathematics and Statistics, University of Jyväskylä P.O. Box 35, 40351 Jyväskylä, Finland pkoskela{at}maths.jyu.fi
Department of Teacher Education, University of Joensuu P.O. Box 55, 57101 Savonlinna, Finland timo.tossavainen{at}joensuu.fi |
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| Abstract: | This paper demonstrates that, in dimensions n  3, the metricboundary of a conformal deformation of the unit ball is pathwiseconnected, and even of bounded turning, provided that the conformalscaling factor satisfies a Harnack inequality and the volumegrowth of the deformed space is at most euclidean. 2000 MathematicsSubject Classification 30C65. |
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