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Conformal Geometry and Dynamics

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Uniform continuity of quasiconformal mappings and conformal deformations


Authors: Pekka Koskela and Tomi Nieminen
Journal: Conform. Geom. Dyn. 12 (2008), 10-17
MSC (2000): Primary 30C65
DOI: https://doi.org/10.1090/S1088-4173-08-00174-4
Published electronically: January 22, 2008
MathSciNet review: 2372760
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Abstract: We prove that quasiconformal maps onto domains satisfying a suitable growth condition on the quasihyperbolic metric are uniformly continuous even when both domains are equipped with internal metric. The improvement over previous results is that the internal metric can be used also in the image domain. We also extend this result for conformal deformations of the euclidean metric on the unit ball of $ \mathbb{R}^n$.


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Additional Information

Pekka Koskela
Affiliation: Department of Mathematics, University of Jyväskylä, P.O. Box 35, FI-40014, Finland
Email: pkoskela@maths.jyu.fi

Tomi Nieminen
Affiliation: Department of Mathematics, University of Jyväskylä, P.O. Box 35, FI-40014, Finland
Email: tominiem@maths.jyu.fi

DOI: https://doi.org/10.1090/S1088-4173-08-00174-4
Keywords: Quasiconformal mapping, conformal metric.
Received by editor(s): April 19, 2007
Published electronically: January 22, 2008
Article copyright: © Copyright 2008 American Mathematical Society

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