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Mat. Sb., 2011, Volume 202, Number 12, Pages 107–112 (Mi msb7801)  

This article is cited in 2 scientific papers (total in 2 papers)

On the measure of conformal difference between Euclidean and Lobachevsky spaces

V. A. Zorich

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

DOI: https://doi.org/10.4213/sm7801

Full text: PDF file (399 kB)
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English version:
Sbornik: Mathematics, 2011, 202:12, 1825–1830

Bibliographic databases:

UDC: 517.54+514.774
MSC: 30C65, 53C42
Received: 25.10.2010

Citation: V. A. Zorich, “On the measure of conformal difference between Euclidean and Lobachevsky spaces”, Mat. Sb., 202:12 (2011), 107–112; Sb. Math., 202:12 (2011), 1825–1830

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb7801
  • https://doi.org/10.4213/sm7801
  • http://mi.mathnet.ru/eng/msb/v202/i12/p107

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Zorich, “Some observations concerning multidimensional quasiconformal mappings”, Sb. Math., 208:3 (2017), 377–398  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. A. Zorich, “Boundary behaviour of automorphisms of a hyperbolic space”, Russian Math. Surveys, 72:4 (2017), 645–670  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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