Freely quasiconformal maps and distance ratio metric

Y. Li; S. Ponnusamy; M. Vuorinen

doi:10.1017/S1446788714000329

Freely quasiconformal maps and distance ratio metric

Complex Variables 2019-02-20 v1

Authors: 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.

Keywords

freely quasiconformal maps distance ratio metric banach spaces homeomorphism quasiconformality metric conditions geometric function theory

Cite

@article{arxiv.1404.0199,
  title  = {Freely quasiconformal maps and distance ratio metric},
  author = {Y. Li and S. Ponnusamy and M. Vuorinen},
  journal= {arXiv preprint arXiv:1404.0199},
  year   = {2019}
}

Comments

10 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1110.6269

Freely quasiconformal maps and distance ratio metric

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