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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Distortion in the spherical metric under quasiconformal mappings
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by Peter A. Hästö PDF
Conform. Geom. Dyn. 7 (2003), 1-10 Request permission


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:
  • 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.
  • © Copyright 2003 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 7 (2003), 1-10
  • MSC (2000): Primary 30C80
  • DOI:
  • MathSciNet review: 1992034