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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Uniform equicontinuity of quasiconformal mappings


Authors: Raimo Näkki and Bruce Palka
Journal: Proc. Amer. Math. Soc. 37 (1973), 427-433
MSC: Primary 30A60
MathSciNet review: 0311900
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Abstract: Necessary and sufficient conditions are given for a family of K-quasiconformal mappings of a fixed domain to be uniformly equicontinuous in that domain, provided the domain has a ``regular'' boundary. Applications to uniformly convergent sequences of quasiconformal mappings are indicated.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0311900-9
PII: S 0002-9939(1973)0311900-9
Keywords: Quasiconformal mapping, uniform domain, uniform equicontinuity, normal family, uniformly convergent sequence
Article copyright: © Copyright 1973 American Mathematical Society