## Mappings of finite distortion: Formation of cusps II

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- by Juhani Takkinen
- Conform. Geom. Dyn.
**11**(2007), 207-218 - DOI: https://doi.org/10.1090/S1088-4173-07-00170-1
- Published electronically: October 18, 2007
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## Abstract:

For $s>0$ given, we consider a planar domain $\Omega _s$ with a rectifiable boundary but containing a cusp of degree $s$, and show that there is no homeomorphism $f\colon \mathbb {R}^2\to \mathbb {R}^2$ of finite distortion with $\exp (\lambda K)\in L^1_{\mathrm {loc}}(\mathbb {R}^2)$ so that $f(B)=\Omega _s$ when $\lambda >4/s$ and $B$ is the unit disc. On the other hand, for $\lambda <2/s$ such an $f$ exists. The critical value for $\lambda$ remains open.## References

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## Bibliographic Information

**Juhani Takkinen**- Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 Finland
- Email: juhani@maths.jyu.fi
- Received by editor(s): May 21, 2007
- Published electronically: October 18, 2007
- Additional Notes: The author was partially supported by the foundation Vilho, Yrjö ja Kalle Väisälän rahasto.
- © Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**11**(2007), 207-218 - MSC (2000): Primary 30C62, 30C65
- DOI: https://doi.org/10.1090/S1088-4173-07-00170-1
- MathSciNet review: 2354095