Extremal length for quasiregular mappings on Heisenberg groups.
In 1957 \textit{B. Fuglede} [Acta. Math. 98, 171--219 (1957; Zbl 0079.27703)] has introduced a notion of the system of exceptional measures. A system of measures \(E\) is said to be exceptional of order \(p\) if its \(p\)-modulus \(M_p(E)\) vanishes. \textit{E. Poletskiĭ} [Mat. Sb., N. Ser. 83(125), 261--272 (1970; Zbl 0207.37603)] was the first who applied this notion to a description of the behavior of a family of curves under a quasiregular mapping (in another terminology a mapping with bounded distortion) in \(\mathbb R^n\). In the present paper we study the behavior of horizontal curves under contact maps and the modulus of a family of horizontal curves under a quasiregular mapping on the Heisenberg group \(\mathbb H^n\).
scientific article; zbMATH DE number 1976009
scientific article