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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Distortion in the spherical metric under quasiconformal mappings


Author: Peter A. Hästö
Journal: Conform. Geom. Dyn. 7 (2003), 1-10
MSC (2000): Primary 30C80
Published electronically: January 23, 2003
MathSciNet review: 1992034
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Abstract: This paper contains bounds for the distortion in the spherical metric, that is to say, bounds for the constant of Hölder continuity of mappings $f \colon ({\mathbb R}^n,q) \to ({\mathbb R}^n, q)$ where $q$ denotes the spherical metric. The mappings considered are $K$-quasiconformal ($K\ge 1$) and satisfy some normalizations or restrictions. All bounds are explicit and asymptotically sharp as $K \to 1$.


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Additional Information

Peter A. Hästö
Affiliation: Department of Mathematics, P.O. Box 4, 00014 University of Helsinki, Finland
Email: peter.hasto@helsinki.fi

DOI: http://dx.doi.org/10.1090/S1088-4173-03-00088-2
PII: S 1088-4173(03)00088-2
Keywords: Spherical chordal metric, distortion, quasiconformal mappings
Received by editor(s): February 11, 2002
Published electronically: January 23, 2003
Additional Notes: Supported in part by The Academy of Finland, Research Contract 12132. I would also like to thank Matti Vuorinen for pointing out this problem to me as well as for advice and suggestions during the process of writing this paper.
Article copyright: © Copyright 2003 American Mathematical Society