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

 

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?)

  • 1. Kari Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994), no. 1, 37–60. MR 1294669 (95m:30028b), http://dx.doi.org/10.1007/BF02392568
  • 2. Kari Astala and Vincenzo Nesi, Composites and quasiconformal mappings: new optimal bounds in two dimensions, Calc. Var. Partial Differential Equations 18 (2003), no. 4, 335–355. MR 2020365 (2005d:74035), http://dx.doi.org/10.1007/s00526-003-0145-9
  • 3. K. Astala, A. Clop, J. Mateu, J. Orobitg and I. Uriarte-Tuero, Distortion of Hausdorff measures and improved Painlevé removability for bounded quasiregular mappings, Duke Math. J., to appear, preprint version: arXiv:math.CV/0609327.
  • 4. C.J. Bishop, Distortion of disks by conformal maps, preprint: http://www.math.sunysb.edu/~bishop/papers/papers.html
  • 5. I. Prause, Distortion of dimension under quasiconformal mappings, Preprint 462, Reports in Mathematics, University of Helsinki, 2007.

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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
Email: istvan.prause@helsinki.fi

DOI: http://dx.doi.org/10.1090/S1088-4173-07-00171-3
PII: S 1088-4173(07)00171-3
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.