Geodesic
Asymptotic behavior at infinity of the admissible growth of the quasiconformality coefficient and the injectivity of immersions of sub-Riemannian manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 81-85

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We determine the asymptotic behavior of the admissible growth of the quasiconformality coefficient in a general global injectivity theorem for immersions of sub-Riemannian manifolds of conformally parabolic type. In the model case of a contact immersion of the Heisenberg group in itself, the asymptotic behavior of the admissible growth of the quasiconformality coefficient for which the mapping is still globally invertible was found by the author earlier. 
@article{TM_2012_279_a6,
     author = {V. A. Zorich},
     title = {Asymptotic behavior at infinity of the admissible growth of the quasiconformality coefficient and the injectivity of immersions of {sub-Riemannian} manifolds},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {81--85},
     publisher = {mathdoc},
     volume = {279},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_279_a6/}
}
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V. A. Zorich. Asymptotic behavior at infinity of the admissible growth of the quasiconformality coefficient and the injectivity of immersions of sub-Riemannian manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 81-85. http://geodesic.mathdoc.fr/item/TM_2012_279_a6/