Ibragimov, Zair Metric density and quasimöbius mappings. (Russian, English) Zbl 1018.30015 Sib. Mat. Zh. 43, No. 5, 1007-1019 (2002); translation in Sib. Math. J. 43, No. 5, 812-821 (2002). Summary: We study the notion of \(\mu\)-density of metric spaces which was introduced by V. V. Aseev and D. A. Trotsenko. An interrelation between the \(\mu\)-density and homogeneous density is established. We also characterize \(\mu\)-dense spaces as “arcwise” connected metric spaces in which “arcs” are the quasimöbius images of the middle-third Cantor set. Finally, we characterize quasiconformal self-mappings of \(\dot{\mathbb R}^n\) in terms of the \(\mu\)-density. Cited in 5 Documents MSC: 30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations Keywords:metric density; quasiconformal mapping; quasimöbius mapping; quasisymmetric embedding; quasiregular mapping; uniformly perfect set PDFBibTeX XMLCite \textit{Z. Ibragimov}, Sib. Mat. Zh. 43, No. 5, 1007--1019 (2002; Zbl 1018.30015); translation in Sib. Math. J. 43, No. 5, 812--821 (2002) Full Text: EuDML