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arXiv · 1404.0199

Freely quasiconformal maps and distance ratio metric

Y. Li·S. Ponnusamy·M. Vuorinen
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Abstract

Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least $2$ and that $D\subset E$ and $D'\subset E'$ are domains. In this paper, we establish, in terms of the $j_D$ metric, a necessary and sufficient condition for the homeomorphism $f: E \to E'$ to be FQC. Moreover, we give, in terms of the $j_D$ metric, a sufficient condition for the homeomorphism $f: D\to D'$ to be FQC. On the other hand, we show that this condition is not necessary.

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Y. Li, S. Ponnusamy, M. Vuorinen. 2014-04-01. Freely quasiconformal maps and distance ratio metric. https://doi.org/10.1017/s1446788714000329

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