Extremal length for quasiregular mappings on Heisenberg groups ✩

In 1957 B. Fuglede (Acta. Math. 98 (1957) 171–219) 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 Mp(E) vanishes. E. Poletskii (Mat. Sb. 83 (1970) 261–272) 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 Rn. 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 Hn.  2003 Elsevier Inc. All rights reserved.