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Generalized quasidisks and conformality II


Author: Chang-Yu Guo
Journal: Proc. Amer. Math. Soc. 143 (2015), 3505-3517
MSC (2010): Primary 30C62, 30C65
Published electronically: February 25, 2015
MathSciNet review: 3348792
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Abstract: We introduce a weaker variant of the concept of three point property, which is equivalent to a non-linear local connectivity condition introduced by the author, Koskela, and Takkinen, sufficient to guarantee the extendability of a conformal map $ f:\mathbb{D}\to \Omega $ to the entire plane as a homeomorphism of locally exponentially integrable distortion. Sufficient conditions for extendability to a homeomorphism of locally $ p$-integrable distortion are also given.


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Chang-Yu Guo
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä, Finland
Email: changyu.c.guo@jyu.fi

DOI: https://doi.org/10.1090/S0002-9939-2015-12449-5
Keywords: Homeomorphism of finite distortion, generalized quasidisk, local connectivity, three point property
Received by editor(s): August 1, 2013
Received by editor(s) in revised form: January 15, 2014
Published electronically: February 25, 2015
Additional Notes: The author was partially supported by the Academy of Finland grant 131477.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2015 American Mathematical Society