Rotational properties of homeomorphisms with integrable distortion
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- by Lauri Hitruhin
- Conform. Geom. Dyn. 22 (2018), 78-98
- DOI: https://doi.org/10.1090/ecgd/321
- Published electronically: August 10, 2018
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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.References
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Bibliographic 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