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Conformal Geometry and Dynamics

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On distortion of Hausdorff measures under quasiconformal mappings

Author: István Prause
Journal: Conform. Geom. Dyn. 11 (2007), 219-223
MSC (2000): Primary 30C62
Published electronically: October 31, 2007
MathSciNet review: 2354096
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Abstract | References | Similar Articles | Additional Information

Abstract: Astala (Acta Math. 173 (1994), no. 1, 37-60) gave optimal bounds for the distortion of Hausdorff dimension under planar quasiconformal maps. The corresponding estimates on the level of Hausdorff measures remain open. We show that these techniques allow for establishing absolute continuity for some weaker Hausdorff measures.

References [Enhancements On Off] (What's this?)

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Additional Information

István Prause
Affiliation: Department of Mathematics and Statistics, P.O. Box 68, FIN-00014 University of Helsinki, Finland
Address at time of publication: Institute of Mathematics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland

Keywords: Quasiconformal, Hausdorff measure
Received by editor(s): August 10, 2007
Published electronically: October 31, 2007
Additional Notes: The author was supported by the Finnish Academy of Science and Letters through Vilho, Yrjö ja Kalle Väisälän rahasto.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.