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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Planar Sobolev homeomorphisms and Hausdorff dimension distortion
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by Tapio Rajala PDF
Proc. Amer. Math. Soc. 139 (2011), 1825-1829 Request permission

Abstract:

We investigate how planar Sobolev-Orlicz homeomorphisms map sets of Hausdorff dimension less than two. With the correct gauge functions the generalized Hausdorff measures of the image sets are shown to be zero.
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Additional Information
  • Tapio Rajala
  • Affiliation: Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland
  • MR Author ID: 838027
  • Email: tapio.m.rajala@jyu.fi
  • Received by editor(s): October 30, 2009
  • Received by editor(s) in revised form: May 28, 2010
  • Published electronically: July 8, 2010
  • Additional Notes: The author acknowledges the support of the Academy of Finland, project No. 211229.
  • Communicated by: Mario Bonk
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1825-1829
  • MSC (2010): Primary 30C65
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10464-1
  • MathSciNet review: 2763769