Skip to Main Content

Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On distortion of Hausdorff measures under quasiconformal mappings
HTML articles powered by AMS MathViewer

by István Prause PDF
Conform. Geom. Dyn. 11 (2007), 219-223 Request permission

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
  • Kari Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994), no. 1, 37–60. MR 1294669, DOI 10.1007/BF02392568
  • 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, DOI 10.1007/s00526-003-0145-9
  • 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.
  • C.J. Bishop, Distortion of disks by conformal maps, preprint: \verb+http://www.math.sunysb.edu/ bishop/papers/papers.html+
  • I. Prause, Distortion of dimension under quasiconformal mappings, Preprint 462, Reports in Mathematics, University of Helsinki, 2007.
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 30C62
  • Retrieve articles in all journals with MSC (2000): 30C62
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
  • 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