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.
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- 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: email@example.com
- 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.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Conform. Geom. Dyn. 11 (2007), 219-223
- MSC (2000): Primary 30C62
- DOI: https://doi.org/10.1090/S1088-4173-07-00171-3
- MathSciNet review: 2354096