# Mappings of finite distortion: Formation of cusps III

@article{Koskela2007MappingsOF, title={Mappings of finite distortion: Formation of cusps III}, author={Pekka Koskela and Juha Takkinen}, journal={Acta Mathematica Sinica, English Series}, year={2007}, volume={26}, pages={817-824} }

We give sharp integrability conditions on the distortion of a planar homeomorphism that maps a standard cusp onto the unit disk.

## 23 Citations

Planar Mappings of Finite Distortion

- Mathematics
- 2011

We review recent results on planar mappings of finite distortion. This class of mappings contains all analytic functions and quasiconformal mappings.

Homeomorphisms of Finite Distortion

- Mathematics
- 2014

In this chapter we establish the optimal regularity of the inverse mapping in higher dimensions and optimal Sobolev regularity for composites. Moreover, we establish optimal moduli of continuity for…

Singularities in L^p-quasidisks

- MathematicsAnnales Fennici Mathematici
- 2021

We study planar domains with exemplary boundary singularities of the form of cusps. A natural question is how much elastic energy is needed to flatten these cusps; that is, to remove singularities.…

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…

Openness and Discreteness

- Mathematics
- 2014

The aim of this chapter is to study conditions under which a mapping of finite distortion is open (maps open sets to open sets) and discrete (preimage of each point is a discrete set).

Stretching multifractal spectra and area compression of homeomorphisms with integrable distortion in higher dimensions

- Mathematics
- 2018

We consider homeomorphisms with integrable distortion in higher dimensions and sharpen the previous bound for area compression, which was presented by Clop and Herron. Our method relies on developing…

Generalized quasidisks and conformality II

- Mathematics
- 2013

We introduce a weaker variant of the concept of three point property, which is equivalent to a non-linear local connectivity condition introduced in [12], sufficient to guarantee the extendability of…

Generalized quasidisks and conformality

- Mathematics
- 2014

We introduce a weaker variant of the concept of linear local connectivity, sufficient to guarantee the extendability of a conformal map f : D → Ω to the entire plane as a homeomorphism of locally…

Integrability of J f and 1∕ J f

- Mathematics
- 2014

In this chapter we study the optimal degree of integrability of J f and 1∕J f for mappings of finite distortion. As an application of our estimates we show that some sets are removable singularities…

Quasiregular curves: Hölder continuity and higher integrability

- MathematicsComplex Analysis and its Synergies
- 2021

We show that a $K$-quasiregular $\omega$-curve from a Euclidean domain to a Euclidean space with respect to a covector $\omega$ is locally $(1/K)(\lVert \omega\rVert/|\omega|_{\ell_1})$-Holder…

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