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Conformal Geometry and Dynamics

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Quasicircles and the conformal group


Authors: Yves Benoist and Dominique Hulin
Journal: Conform. Geom. Dyn. 20 (2016), 197-217
MSC (2010): Primary 30C62; Secondary 57M60
DOI: https://doi.org/10.1090/ecgd/297
Published electronically: May 25, 2016
Revised article: Conform. Geom. Dyn. 20 (2016), 282-302
MathSciNet review: 3504811
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Abstract:

The article "Quasicircles and the conformal group" by Yves Benoist and Dominique Hulin (Conformal Geometry and Dynamics 20 (2016), no. 10, 197-217) was retracted by the authors in September 2016 because the findings had been previously published.

We prove that a Jordan curve in the 2-sphere is a quasicircle if and only if the closure of its orbit under the action of the conformal group contains only points and Jordan curves.


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Additional Information

Yves Benoist
Affiliation: Department of Mathematics, Université Paris-Sud, Orsay 91405, France
Email: yves.benoist@math.u-psud.fr

Dominique Hulin
Affiliation: Department of Mathematics, Université Paris-Sud, Orsay 91405, France
Email: dominique.hulin@math.u-psud.fr

DOI: https://doi.org/10.1090/ecgd/297
Keywords: Quasidisks, quasiconformal maps, Jordan curves
Received by editor(s): September 1, 2015
Published electronically: May 25, 2016
Article copyright: © Copyright 2016 American Mathematical Society