Geodesic
On the measure of conformal difference between Euclidean and Lobachevsky spaces
Sbornik. Mathematics, Tome 202 (2011) no. 12, pp. 1825-1830

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Euclidean space $\mathbb R^n$ and Lobachevsky space $\mathbb H^n$ are known to be not equivalent either conformally or quasiconformally. In this work we give exact asymptotics of the critical order of growth at infinity for the quasiconformality coefficient of a diffeomorphism $f\colon \mathbb R^n\to\mathbb H^n$ for which such a mapping $f$ is possible. We also consider the general case of immersions $f\colon M^n\to N^n$ of conformally parabolic Riemannian manifolds. Bibliography: 17 titles.
Keywords: quasiconformal mapping, Riemannian manifold, conformal type of a Riemannian manifold, Euclidean space, Lobachevsky space. 
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     author = {V. A. Zorich},
     title = {On the measure of conformal difference between {Euclidean} and {Lobachevsky} spaces},
     journal = {Sbornik. Mathematics},
     pages = {1825--1830},
     publisher = {mathdoc},
     volume = {202},
     number = {12},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_12_a3/}
}
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V. A. Zorich. On the measure of conformal difference between Euclidean and Lobachevsky spaces. Sbornik. Mathematics, Tome 202 (2011) no. 12, pp. 1825-1830. http://geodesic.mathdoc.fr/item/SM_2011_202_12_a3/