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Asymptotic behavior at infinity of the admissible growth of the quasiconformality coefficient and the injectivity of immersions of sub-Riemannian manifolds

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Abstract

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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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    V. A. Zorich

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  1. V. A. Zorich
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Correspondence to V. A. Zorich.

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Original Russian Text © V.A. Zorich, 2012, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Vol. 279, pp. 81–85.

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Zorich, V.A. Asymptotic behavior at infinity of the admissible growth of the quasiconformality coefficient and the injectivity of immersions of sub-Riemannian manifolds. Proc. Steklov Inst. Math. 279, 73–77 (2012). https://doi.org/10.1134/S008154381208007X

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  • DOI: https://doi.org/10.1134/S008154381208007X

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