Publicacions Matemàtiques

Generalized quasidisks and conformality

Chang-Yu Guo, Pekka Koskela, and Juhani Takkinen

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Abstract

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.

Article information

Source
Publ. Mat., Volume 58, Number 1 (2014), 193-212.

Dates
First available in Project Euclid: 20 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.pm/1387570396

Mathematical Reviews number (MathSciNet)
MR3161514

Zentralblatt MATH identifier
1286.30021

Subjects
Primary: 30C62: Quasiconformal mappings in the plane 30C65: Quasiconformal mappings in $R^n$ , other generalizations

Keywords
Homeomorphism of finite distortion

Citation

Guo, Chang-Yu; Koskela, Pekka; Takkinen, Juhani. Generalized quasidisks and conformality. Publ. Mat. 58 (2014), no. 1, 193--212. https://projecteuclid.org/euclid.pm/1387570396


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