• DOI:10.1090/ECGD/321
• Corpus ID: 52042751

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. 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
p

-integrable distortion is sharp in this strong sense.