Freely quasiconformal maps and distance ratio metric

Abstract

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

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

References in corpus (2)

• Local Convexity Properties of Quasihyperbolic Balls in Punctured Space
• On Quasihyperbolic Geodesics in Banach Spaces

Cited by in corpus (1)

• A note on Väisälä's problem concerning free quasiconformal mappings