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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.

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Rotational properties of homeomorphisms with integrable distortion
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by Lauri Hitruhin PDF
Conform. Geom. Dyn. 22 (2018), 78-98 Request permission

Abstract:

We establish a modulus inequality, with weak assumptions on the Sobolev regularity, for homeomorphisms with integrable distortion. As an application, we find upper bounds for the pointwise rotation of planar homeomorphisms with $p$-integrable distortion. When the mapping is entire we bound the local pointwise rotation and when the mapping is restricted to a bounded convex domain $\Omega \subset \mathbb {C}$ we concentrate on the rotation along the boundary. Furthermore, we show that these bounds are sharp in a very strong sense. Our examples will also prove that the modulus of continuity result, due to Koskela and Takkinen, for the homeomorphisms with $p$-integrable distortion is sharp in this strong sense.
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Additional Information
  • Lauri Hitruhin
  • Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014 University of Helsinki, Finland
  • MR Author ID: 1173526
  • Email: lauri.hitruhin@helsinki.fi
  • Received by editor(s): April 28, 2017
  • Received by editor(s) in revised form: November 17, 2017
  • Published electronically: August 10, 2018
  • Additional Notes: The author was financially supported by the Väisälä Foundation and by The Centre of Excellence in Analysis and Dynamics Research (Academy of Finland, decision 271983)
  • © Copyright 2018 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 22 (2018), 78-98
  • MSC (2010): Primary 30C65
  • DOI: https://doi.org/10.1090/ecgd/321
  • MathSciNet review: 3841858