Quasiregular mappings of the Heisenberg group (Q1196015)

A Picard type theorem is proved for quasiregular maps of the \((2m+1)\)- dimensional Heisenberg group \(H_ m\) into \((2m+1)\)-manifolds \(M=N\backslash\{a_ 1,\dots,a_ q\}\), where \(N\) is compact and \(M\) is given an arbitrary Riemannian metric. Surprisingly, there exists a nonconstant quasiregular map of \(H_ 1\) into \(\mathbb{R}^ 3\backslash\{0\}\), and consequently of \(H_ 1\) into \(\mathbb{R}^ 3\backslash\{a_ 1,\dots,a_ q\}\) when earlier constructions are combined, but there exists no such map of \(H_ m\) into \(H_ m\backslash\{a\}\), \(a\in H_ m\).