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