Boundary behavior of conformal deformations
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- by Tomi Nieminen and Timo Tossavainen PDF
- Conform. Geom. Dyn. 11 (2007), 56-64 Request permission
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.References
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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
- Received by editor(s): October 20, 2006
- Published electronically: May 30, 2007
- © Copyright 2007 American Mathematical Society
- Journal: Conform. Geom. Dyn. 11 (2007), 56-64
- MSC (2000): Primary 30C65
- DOI: https://doi.org/10.1090/S1088-4173-07-00161-0
- MathSciNet review: 2314242