Mappings with bounded distortion on the Heisenberg group. (Q1432103)

The paper deals with the theories of quasiconformal (qc) and quasiregular (qr) mappings on the Heisenberg group, with the intention to generalize results that are well-known in the Euclidean spaces. The author remarks that at present the theory of qc maps is almost as complete as in the Euclidean situation whereas in the case of noninjective qr maps some unnatural smoothness conditions have been required. The author's aim is to find a better and more natural definition of qr maps. In the Euclidean case this definition is due to Yu. G. Reshetnyak. Several basic properties of maps qr in the sense of the author are stated.