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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 3, Pages 37–48 (Mi faa310)  

This article is cited in 15 scientific papers (total in 15 papers)

Quasiconformal Immersions of Riemannian Manifolds and a Picard Type Theorem

V. A. Zorich

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

Abstract: We study singularities of quasiconformal immersions of Riemannian manifolds and show that the phenomenon of compulsory continuation holds in dimension $n\ge3$. In particular, this result in a stronger version of the Picard theorem—one without omitted values.

DOI: https://doi.org/10.4213/faa310

Full text: PDF file (289 kB)
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English version:
Functional Analysis and Its Applications, 2000, 34:3, 188–196

Bibliographic databases:

UDC: 517.54+514.774
Received: 18.12.1998

Citation: V. A. Zorich, “Quasiconformal Immersions of Riemannian Manifolds and a Picard Type Theorem”, Funktsional. Anal. i Prilozhen., 34:3 (2000), 37–48; Funct. Anal. Appl., 34:3 (2000), 188–196

Citation in format AMSBIB
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\paper Quasiconformal Immersions of Riemannian Manifolds and a Picard Type Theorem
\jour Funktsional. Anal. i Prilozhen.
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\pages 37--48
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\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 3
\pages 188--196
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Zorich, “Removable singularity of a quasi-conformal immersion”, Russian Math. Surveys, 56:4 (2001), 772–773  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Zorich, “Three Remarks on the Inversion Problem for Polynomial Maps”, Proc. Steklov Inst. Math., 235 (2001), 87–90  mathnet  mathscinet  zmath
    3. V. A. Zorich, “Quasi-conformal maps and the asymptotic geometry of manifolds”, Russian Math. Surveys, 57:3 (2002), 437–462  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. A. Zorich, “Asymptotics at infinity of the admissible growth of the quasi-conformality coefficient and the injectivity of immersions of Riemannian manifolds”, Russian Math. Surveys, 58:3 (2003), 624–626  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Holopainen, I, “Mappings of finite distortion: Global homeomorphism theorem”, Annales Academiae Scientiarum Fennicae-Mathematica, 29:1 (2004), 59  mathscinet  zmath  isi
    6. V. A. Zorich, “On contact quasi-conformal immersions”, Russian Math. Surveys, 60:2 (2005), 382–384  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. V. A. Zorich, “Contact Quasiconformal Immersions”, Proc. Steklov Inst. Math., 253 (2006), 71–77  mathnet  crossref  mathscinet  elib
    8. V. A. Zorich, “Global homeomorphism theorem for conformally hyperbolic manifolds”, Russian Math. Surveys, 62:4 (2007), 826–828  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Pankka, P, “Slow quasiregular mappings and universal coverings”, Duke Mathematical Journal, 141:2 (2008), 293  crossref  mathscinet  zmath  isi  elib  scopus
    10. V. A. Zorich, “A non-removable singularity of a quasi-conformal immersion”, Russian Math. Surveys, 64:1 (2009), 173–174  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. V. A. Zorich, “On the measure of conformal difference between Euclidean and Lobachevsky spaces”, Sb. Math., 202:12 (2011), 1825–1830  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. V. A. Zorich, “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 (2012), 73–77  mathnet  crossref  mathscinet  isi  elib  elib
    13. Namazi H., Pankka P., Souto J., “Distributional Limits of Riemannian Manifolds and Graphs With Sublinear Genus Growth”, Geom. Funct. Anal., 24:1 (2014), 322–359  crossref  mathscinet  zmath  isi  scopus
    14. Frances Ch., “Removable and Essential Singular Sets For Higher Dimensional Conformal Maps”, Comment. Math. Helv., 89:2 (2014), 405–441  crossref  mathscinet  zmath  isi  scopus
    15. D. P. Il'yutko, E. A. Sevost'yanov, “Open discrete mappings with unbounded coefficient of quasi-conformality on Riemannian manifolds”, Sb. Math., 207:4 (2016), 537–580  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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