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Mat. Sb. (N.S.), 1967, Volume 74(116), Number 3, Pages 417–433 (Mi msb4170)  

This article is cited in 34 scientific papers (total in 35 papers)

A theorem of M. A. Lavrent'ev on quasiconformal space maps

V. A. Zorich


Full text: PDF file (2789 kB)

English version:
Mathematics of the USSR-Sbornik, 1967, 3:3, 389–403

Bibliographic databases:

UDC: 517.54
MSC: 30C62, 28A05, 57S10, 30D30
Received: 20.06.1967

Citation: V. A. Zorich, “A theorem of M. A. Lavrent'ev on quasiconformal space maps”, Mat. Sb. (N.S.), 74(116):3 (1967), 417–433; Math. USSR-Sb., 3:3 (1967), 389–403

Citation in format AMSBIB
\Bibitem{Zor67}
\by V.~A.~Zorich
\paper A theorem of M.\,A.~Lavrent'ev on quasiconformal space maps
\jour Mat. Sb. (N.S.)
\yr 1967
\vol 74(116)
\issue 3
\pages 417--433
\mathnet{http://mi.mathnet.ru/msb4170}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=223569}
\zmath{https://zbmath.org/?q=an:0184.10801|0181.08701}
\transl
\jour Math. USSR-Sb.
\yr 1967
\vol 3
\issue 3
\pages 389--403
\crossref{https://doi.org/10.1070/SM1967v003n03ABEH002751}


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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, “An isolated singularity of mappings with bounded distortion”, Math. USSR-Sb., 10:4 (1970), 581–583  mathnet  crossref  mathscinet  zmath
    2. E. A. Poletskii, “On the removal of singularities of quasiconformal mappings”, Math. USSR-Sb., 21:2 (1973), 240–254  mathnet  crossref  mathscinet  zmath
    3. Marius Radulescu, Sorin Radulescu, “Global inversion theorems and applications to differential equations”, Nonlinear Analysis: Theory, Methods & Applications, 4:5 (1980), 951  crossref
    4. Vuorinen M., “Conformal Geometry and Quasiregular-Mappings”, Lect. Notes Math., 1319 (1988), 1–&  isi
    5. Zorich V., “The Global Homeomorphism Theorem for Space Quasi-Conformal Mappings, its Development and Related Open Problems”, Lect. Notes Math., 1508 (1992), 132–148  isi
    6. I. V. Zhuravlev, “Sufficient conditions for local quasiconformality of mappings with bounded distortion”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 437–445  mathnet  crossref  mathscinet  zmath
    7. M. Vuorinen, O. Martio, V. I. Ryazanov, “On the local behaviour of quasi-regular space mappings”, Izv. Math., 62:6 (1998), 1207–1220  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. V. A. Zorich, “Quasiconformal embeddings of Riemannian manifolds and a Picard-type theorem”, Russian Math. Surveys, 53:1 (1998), 227–228  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    9. V. A. Zorich, “Quasiconformal Immersions of Riemannian Manifolds and a Picard Type Theorem”, Funct. Anal. Appl., 34:3 (2000), 188–196  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. V. A. Zorich, “Three Remarks on the Inversion Problem for Polynomial Maps”, Proc. Steklov Inst. Math., 235 (2001), 87–90  mathnet  mathscinet  zmath
    11. 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
    12. Zhuravlev I., “Smoothing Mappings with Bounded Distortion”, Dokl. Math., 65:1 (2002), 51–53  isi
    13. 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
    14. 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
    15. V. A. Zorich, “Contact Quasiconformal Immersions”, Proc. Steklov Inst. Math., 253 (2006), 71–77  mathnet  crossref  mathscinet  elib
    16. Markina, I, “On value distributions for quasimeromorphic mappings on H-type Carnot groups”, Bulletin Des Sciences Mathematiques, 130:6 (2006), 467  crossref  isi
    17. 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
    18. E. A. Sevost'yanov, “Towards a theory of removable singularities for maps with unbounded characteristic of quasi-conformity”, Izv. Math., 74:1 (2010), 151–165  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. V. A. Zorich, “Asymptotic behaviour at infinity of the admissible growth of the quasi-conformality coefficient and the invertibility of contact immersions of the Heisenberg group”, Russian Math. Surveys, 65:3 (2010), 591–592  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    20. R. R. Salimov, E. A. Sevost'yanov, “The theory of shell-based $Q$-mappings in geometric function theory”, Sb. Math., 201:6 (2010), 909–934  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. E. A. Sevost'yanov, “On the branch points of mappings with the unbounded coefficient of quasiconformality”, Siberian Math. J., 51:5 (2010), 899–912  mathnet  crossref  mathscinet  isi  elib
    22. 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
    23. Walter Bergweiler, “Iteration of Quasiregular Mappings”, Comput. Methods Funct. Theory, 10:2 (2011), 455  crossref
    24. Sevostyanov E.A., Salimov R.R., “Analog teoremy lavrenteva - zoricha o globalnom gomeomorfizme dlya otobrazhenii s neogranichennoi kharakteristikoi”, Vestnik volgogradskogo gosudarstvennogo universiteta. seriya 1: matematika. fizika, 2011, no. 2, 80–90  elib
    25. A. N. Kondrashov, “On the theory of degenerate alternating Beltrami equations”, Siberian Math. J., 53:6 (2012), 1061–1074  mathnet  crossref  mathscinet  isi  elib  elib
    26. 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
    27. Walter Bergweiler, D.A.. Nicks, “Foundations for an iteration theory of entire quasiregular maps”, Isr. J. Math, 2014  crossref
    28. Cristea M., “Local Homeomorphisms Satisfying Generalized Modular Inequalities”, Complex Var. Elliptic Equ., 59:10 (2014), 1363–1387  crossref  isi
    29. Alastair Fletcher, Douglas Macclure, “On Quasiregular Linearizers”, Comput. Methods Funct. Theory, 2015  crossref
    30. David Drasin, Pekka Pankka, “Sharpness of Rickman’s Picard theorem in all dimensions”, Acta Math, 214:2 (2015), 209  crossref
    31. V. A. Zorich, “A note on the injectivity radius of quasiconformal immersions”, Russian Math. Surveys, 71:1 (2016), 161–163  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    32. V. A. Zorich, “Some observations concerning multidimensional quasiconformal mappings”, Sb. Math., 208:3 (2017), 377–398  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    33. 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
    34. A. I. Aptekarev, V. M. Buchstaber, V. A. Vassiliev, M. L. Gromov, Yu. S. Ilyashenko, B. S. Kashin, V. M. Keselman, V. V. Kozlov, M. L. Kontsevich, I. M. Krichever, N. G. Kruzhilin, S. K. Lando, Yu. I. Manin, G. A. Margulis, S. Yu. Nemirovski, S. P. Novikov, Yu. G. Reshetnyak, Ya. G. Sinai, S. P. Suetin, D. V. Treschev, D. B. Fuchs, A. G. Khovanskii, E. M. Chirka, A. S. Schwarz, A. N. Shiryaev, “Vladimir Antonovich Zorich (on his 80th birthday)”, Russian Math. Surveys, 73:5 (2018), 935–939  mathnet  crossref  crossref  adsnasa  isi  elib
    35. Apanasov B.N., “Topological Barriers For Locally Homeo-Morphic Quasiregular Mappings in 3-Space”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 43 (2018), 579–596  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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