# Rotational properties of homeomorphisms with integrable distortion

@article{Hitruhin2018RotationalPO,
title={Rotational properties of homeomorphisms with integrable distortion},
author={Lauri Hitruhin},
journal={Conformal Geometry and Dynamics of the American Mathematical Society},
year={2018}
}
• L. Hitruhin
• Published 10 August 2018
• Mathematics
• Conformal Geometry and Dynamics of the American Mathematical Society
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 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 Ω ⊂ C \Omega \subset \mathbb {C} we concentrate on the rotation along the boundary…
6 Citations

## Figures from this paper

Fe b 20 21 Rotation bounds for Hölder continuous homeomorphisms with integrable distortion
• Mathematics
• 2021
We obtain sharp rotation bounds for the subclass of homeomorphisms f : C → C of finite distortion which have distortion function in Lploc, p > 1, and for which a Hölder continuous inverse is
Pointwise rotation for homeomorphisms with integrable distortion and controlled compression
• Mathematics
• 2021
We obtain sharp rotation bounds for homeomorphisms f : C → C whose distortion is in Lploc, p ≥ 1, and whose inverse have controlled modulus of continuity. The interest in this class is partially
On mappings of finite distortion that are quasiconformal in the unit disk
• Mathematics
• 2021
We study quasiconformal mappings of the unit disk that have homeomorphic planar extension with controlled distortion. For these mappings we prove a bound for the modulus of continuity of the inverse
Joint rotational and stretching multifractal spectra of mappings with integrable distortion
• L. Hitruhin
• Mathematics
Revista Matemática Iberoamericana
• 2019
We establish bounds for both the stretching and the rotational multifractal spectra of planar homeomorphic mappings with p-integrable distortion. Moreover, we show that these bounds are sharp by
Dimension compression and expansion under homeomorphisms with exponentially integrable distortion
. We improve both dimension compression and expansion bounds for homeomorphisms with p -exponentially integrable distortion. To the ﬁrst direction we also introduce estimates for the compression
Rotation bounds for H\"older continuous homeomorphisms with integrable distortion
• Mathematics
• 2021
We obtain sharp rotation bounds for the subclass of homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ of finite distortion which have distortion function in $L^p_{loc}$, $p>1$, and for which a Holder

## References

SHOWING 1-10 OF 15 REFERENCES
ON Q-HOMEOMORPHISMS
• Mathematics
• 2005
Space BMO-quasiconformal mappings satisfy a special modulus inequality that is used to dene the class of Q-homeomorphisms. In this class we study distortion theorems, boundary behavior, removability
Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)
• Mathematics
• 2009
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.
Bilipschitz and quasiconformal rotation, stretching and multifractal spectra
• Mathematics
• 2015
We establish sharp bounds for simultaneous local rotation and Hölder-distortion of planar quasiconformal maps. In addition, we give sharp estimates for the corresponding joint quasiconformal
Pointwise rotation for mappings with exponentially integrable distortion
We prove an upper bound for pointwise rotation of mappings with $p$-exponentially integrable distortion. We also show that this bound is essentially optimal by providing examples which attain this
Mappings of finite distortion: Formation of cusps III
• Mathematics
• 2007
We give sharp integrability conditions on the distortion of a planar homeomorphism that maps a standard cusp onto the unit disk.
Extremal Mappings of Finite Distortion
• Mathematics
• 2005
The theory of mappings of finite distortion has arisen out of a need to extend the ideas and applications of the classical theory of quasiconformal mappings to the degenerate elliptic setting where
Lectures on Mappings of Finite Distortion
• Mathematics
• 2014
Introduction.- Continuity.- Openness and discreteness.- Images and preimages of null sets.- Homeomorphisms of finite distortion.- Integrability of Jf and 1/Jf.- Final comments.- Appendix.- References.
Lectures on n-Dimensional Quasiconformal Mappings
The modulus of a curve family.- Quasiconformal mappings.- Background in real analysis.- The analytic properties of quasiconformal mappings.- Mapping problems.
Mappings of finite distortion: Capacity and modulus inequalities
• Mathematics
• 2006
Abstract We establish capacity and modulus inequalities for mappings of finite distortion under minimal regularity assumptions.
A note on planar homeomorphisms
• Rend. Accad. Sci. Fis. Mat. Napoli (4)
• 2008