# Stretching and rotation sets of quasiconformal mappings

@article{Bongers2019StretchingAR, title={Stretching and rotation sets of quasiconformal mappings}, author={Tyler Bongers}, journal={Annales Academiae Scientiarum Fennicae Mathematica}, year={2019} }

Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such maps have many useful geometric distortion properties, and yield a flexible and powerful generalization of conformal mappings. In this work, we study the singularities of these maps, in particular the sizes of the sets where a quasiconformal map can exhibit given stretching and rotation behavior. We…

## 5 Citations

Existence of quasiconformal maps with maximal stretching on any given countable set

- Mathematics
- 2021

Abstract. Quasiconformal maps are homeomorphisms with useful local distortion inequalities; infinitesimally, they map balls to ellipsoids with bounded eccentricity. This leads to a number of useful…

Improved Hölder continuity of quasiconformal maps

- MathematicsAnnales Academiae Scientiarum Fennicae Mathematica
- 2019

Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local…

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…

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…

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