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Conformal Geometry and Dynamics

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Rotational properties of homeomorphisms with integrable distortion


Author: Lauri Hitruhin
Journal: Conform. Geom. Dyn. 22 (2018), 78-98
MSC (2010): Primary 30C65
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.


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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
Email: lauri.hitruhin@helsinki.fi

DOI: https://doi.org/10.1090/ecgd/321
Keywords: Mappings of finite distortion, rotation, integrable distortion
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)
Article copyright: © Copyright 2018 American Mathematical Society

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