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

 

Boundary behavior of conformal deformations


Authors: Tomi Nieminen and Timo Tossavainen
Journal: Conform. Geom. Dyn. 11 (2007), 56-64
MSC (2000): Primary 30C65
Published electronically: May 30, 2007
MathSciNet review: 2314242
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Abstract: We study conformal deformations of the Euclidean metric in the unit ball $ \mathbb{B}^{n}$. We assume that the density associated with the deformation satisfies a Harnack inequality and an arbitrary volume growth condition on the isodiametric profile. We establish a Hausdorff (gauge) dimension estimate for the set $ E\subset \partial \mathbb{B}^{n}$ where such a deformation mapping can ``blow up''. We also prove a generalization of Gerasch's theorem in our setting.


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Additional Information

Tomi Nieminen
Affiliation: Department of Mathematics and Statistics, Jyväskylä University, P.O. Box 35, FIN-40014 Jyväskylä, Finland
Email: tominiem@maths.jyu.fi

Timo Tossavainen
Affiliation: Department of Teacher Education, University of Joensuu, P.O. Box 86, FIN-57101 Savonlinna, Finland
Email: timo.tossavainen@joensuu.fi

DOI: http://dx.doi.org/10.1090/S1088-4173-07-00161-0
PII: S 1088-4173(07)00161-0
Keywords: Boundary, conformal metrics, quasiconformal mapping.
Received by editor(s): October 20, 2006
Published electronically: May 30, 2007
Article copyright: © Copyright 2007 American Mathematical Society