Quasiregular Mappings on Sub-Riemannian Manifolds

摘要: We study mappings on sub-Riemannian manifolds which are quasiregular with respect to the Carnot–Caratheodory distances and discuss several related notions. On H-type Carnot groups, have been introduced earlier using an analytic definition, but so far, a good working definition in same spirit is not available setting of general manifolds. In present paper we adopt therefore metric rather than viewpoint. As first main result, prove that lens space admits nontrivial uniformly (UQR) mappings, is, uniform bound distortion all iterates. doing so, also obtain new examples UQR maps standard spheres. The proof based method for building conformal traps spheres quasiconformal flows, adaptation this approach quotients One may then semigroup generated by mapping. second part follow Tukia existence measurable structure invariant under such semigroup. Here, specified only horizontal distribution, pullback defined Margulis–Mostow derivative (which generalizes classical Pansu derivatives).