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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Planar Sobolev homeomorphisms and Hausdorff dimension distortion


Author: Tapio Rajala
Journal: Proc. Amer. Math. Soc. 139 (2011), 1825-1829
MSC (2010): Primary 30C65
Published electronically: July 8, 2010
MathSciNet review: 2763769
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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
Email: tapio.m.rajala@jyu.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10464-1
PII: S 0002-9939(2010)10464-1
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.