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The cardinality of quasiconformally nonequivalent topological $ 3$-balls with flat boundaries is $ \mathfrak{c}$

Author: Raimo Näkki
Journal: Proc. Amer. Math. Soc. 75 (1979), 63-68
MSC: Primary 30C60
MathSciNet review: 529214
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Abstract: The theorem mentioned in the title is proved. During the course of the proof, the failure for $ n = 3$ of the following 2-dimensional result will also be established: The boundary of a Jordan domain D in n-space is a quasiconformal $ (n - 1)$-sphere if every quasiconformal self-mapping of D can be extended to a quasiconformal self-mapping of the whole space.

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Keywords: Cardinality, quasiconformal mapping, modulus of a curve family, topological ball, quasiconformal sphere, flat boundary
Article copyright: © Copyright 1979 American Mathematical Society

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