Uniformly Quasiregular Maps on the Compactified Heisenberg Group

摘要: We show the existence of a non-injective uniformly quasiregular mapping acting on one-point compactification \(\bar{ {\mathbb{H}}}^{1}={\mathbb{H}}^{1}\cup\{\infty\}\) Heisenberg group ℍ1 equipped with sub-Riemannian metric. The corresponding statement for arbitrary mappings sphere \({\mathbb{S}}^{n} \) was proven by Martin (Conform. Geom. Dyn. 1:24–27, 1997). Moreover, we construct {\mathbb{H}}}^{1}\) large-dimensional branch sets. prove that any map g there exists measurable CR structure μ which is equivariant under semigroup Γ generated g. This equivalent to an horizontal conformal structure.