Generalized quasidisks and conformality II

Guo, Chang-Yu

doi:10.1090/S0002-9939-2015-12449-5

Generalized quasidisks and conformality II
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by Chang-Yu Guo

Proc. Amer. Math. Soc. 143 (2015), 3505-3517

DOI: https://doi.org/10.1090/S0002-9939-2015-12449-5

Published electronically: February 25, 2015

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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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