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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

Timo Tossavainen
Affiliation: Department of Teacher Education, University of Joensuu, P.O. Box 86, FIN-57101 Savonlinna, Finland

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