## Uniform continuity of quasiconformal mappings and conformal deformations

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- by Pekka Koskela and Tomi Nieminen PDF
- Conform. Geom. Dyn.
**12**(2008), 10-17 Request permission

## 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 $\mathbb {R}^n$.## References

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## Additional Information

**Pekka Koskela**- Affiliation: Department of Mathematics, University of Jyväskylä, P.O. Box 35, FI-40014, Finland
- MR Author ID: 289254
- 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
- Received by editor(s): April 19, 2007
- Published electronically: January 22, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**12**(2008), 10-17 - MSC (2000): Primary 30C65
- DOI: https://doi.org/10.1090/S1088-4173-08-00174-4
- MathSciNet review: 2372760