Open Access
2014 Generalized quasidisks and conformality
Chang-Yu Guo, Pekka Koskela, Juhani Takkinen
Publ. Mat. 58(1): 193-212 (2014).


We introduce a weaker variant of the concept of linear local connectivity, sufficient to guarantee the extendability of a conformal map $f\colon\mathbb D\to\Omega$ to the entire plane as a homeomorphism of locally exponentially integrable distortion. Additionally, we show that a conformal map as above cannot necessarily be extended in this manner if we assume that $\Omega$ is the image of $\mathbb D$ under a self-homeomorphism of the plane that has locally exponentially integrable distortion.


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Chang-Yu Guo. Pekka Koskela. Juhani Takkinen. "Generalized quasidisks and conformality." Publ. Mat. 58 (1) 193 - 212, 2014.


Published: 2014
First available in Project Euclid: 20 December 2013

zbMATH: 1286.30021
MathSciNet: MR3161514

Primary: 30C62 , 30C65

Keywords: Homeomorphism of finite distortion

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. 1 • 2014
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