Geodesic
Asymptotic behavior at infinity of the admissible growth of the quasiconformality coefficient and the injectivity of immersions of sub-Riemannian manifolds
Informatics and Automation, 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. 
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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. Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 81-85. http://geodesic.mathdoc.fr/item/TRSPY_2012_279_a6/

[1] Lavrentev M. A., “Ob odnom differentsialnom priznake gomeomorfnykh otobrazhenii trekhmernykh oblastei”, DAN SSSR, 20 (1938), 241–242

[2] Zorich V. A., “Teorema M. A. Lavrenteva o kvazikonformnykh otobrazheniyakh prostranstva”, Mat. sb., 74(116):3 (1967), 417–433 | MR | Zbl

[3] Zorich V. A., “The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems”, Quasiconformal space mappings, Lect. Notes Math., 1508, Springer, Berlin, 1992, 132–148 | DOI | MR

[4] Zorich V. A., “Kvazikonformnye otobrazheniya i asimptoticheskaya geometriya mnogoobrazii”, UMN, 57:3 (2002), 3–28 | DOI | MR | Zbl

[5] Zorich V. A., “Dopustimyi poryadok rosta koeffitsienta kvazikonformnosti v teoreme M. A. Lavrenteva”, DAN SSSR, 181:3 (1968), 530–533 | Zbl

[6] Gromov M., “Hyperbolic manifolds, groups and actions”, Riemann surfaces and related topics, Proc. Conf. (Stony Brook, 1978), Ann. Math. Stud., 97, Princeton Univ. Press, Princeton, NJ, 1981, 183–213 | MR

[7] Gromov M., Metric structures for Riemannian and non-Riemannian spaces, With appendices by M. Katz, P. Pansu, S. Semmes, Birkhäuser, Boston, 1999 | MR | Zbl

[8] Zorich V. A., “Kvazikonformnye pogruzheniya rimanovykh mnogoobrazii i teorema pikarovskogo tipa”, Funkts. analiz i ego pril., 34:3 (2000), 37–48 | DOI | MR | Zbl

[9] Zorich V. A., “Asimptotika dopustimogo rosta koeffitsienta kvazikonformnosti v beskonechnosti i in'ektivnost pogruzhenii rimanovykh mnogoobrazii”, UMN, 58:3 (2003), 191–192 | DOI | MR | Zbl

[10] Zorich V. A., “Asymptotics of the admissible growth of the coefficient of quasiconformality at infinity and injectivity of immersions of Riemannian manifolds”, Publ. Inst. Math. Nouv. Sér., 75 (2004), 53–57 | DOI | MR | Zbl

[11] Zorich V. A., “Asymptotic geometry and conformal types of Carnot–Carathéodory spaces”, Geom. Funct. Anal., 9:2 (1999), 393–411 | DOI | MR | Zbl

[12] Zorich V. A., “O kontaktnykh kvazikonformnykh pogruzheniyakh”, UMN, 60:2 (2005), 161–162 | DOI | MR | Zbl

[13] Zorich V. A., “Kontaktnye kvazikonformnye pogruzheniya”, Tr. MIAN, 253, 2006, 81–87 | MR

[14] Zorich V. A., Keselman V. M., “O konformnom tipe rimanova mnogoobraziya”, Funkts. analiz i ego pril., 30:2 (1996), 40–55 | DOI | MR | Zbl

[15] Zorich V. A., “Asimptotika dopustimogo rosta koeffitsienta kvazikonformnosti v beskonechnosti i obratimost kontaktnykh pogruzhenii gruppy Geizenberga”, UMN, 65:3 (2010), 191–192 | DOI | MR | Zbl

[16] Mazya V. G., Prostranstva S. L. Soboleva, Izd-vo LGU, L., 1985 | MR | Zbl

[17] Grigor'yan A., “Isoperimetric inequalities and capacities on Riemannian manifolds”, The Maz'ya anniversary collection, v. 1, Oper. Theory: Adv. Appl., 109, Birkhäuser, Basel, 1999, 139–153 | MR | Zbl