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Siberian Mathematical Journal

, Volume 25, Issue 1, pp 15–23 | Cite as

Convergence and stability of bounded modulus distortion mappings

  • V. V. Aseev
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Literature Cited

  1. 1.
    J. Väisälä, Lectures on n-Dimensional Quasiconformal Mappings Springer-Verlag, Berlin (1971).Google Scholar
  2. 2.
    F. Caraman, n-Dimensional Quasiconformal (QCf) Mappings, Editura Academici Bucuresti, Abacus Press, Tunbridge Wells, Kent (1974).Google Scholar
  3. 3.
    A. K. Varisov, “The extension of spatial quasiconformal mappings,” Dokl. Akad. Nauk SSSR,234, No. 4, 740–742 (1977).Google Scholar
  4. 4.
    V. V. Aseev and A. K. Varisov, “A quasiconformality test for mappings of smooth surfaces,” Dokl. Akad. Nauk SSSR,234, No. 5, 1001–1003 (1977).Google Scholar
  5. 5.
    V. V. Aseev, “Homeomorphisms of k-dimensional spheres preserving n-dimensional spatial moduli,” Dokl. Akad. Nauk SSSR,243, No. 6, 1357–1360 (1978).Google Scholar
  6. 6.
    F. W. Gehring, “The Caratheodory convergence theorem for quasiconformal mappings in space,” Ann. Acad. Sci. Fenn., Ser. AI,336, No. 11, 1–21 (1963).Google Scholar
  7. 7.
    G. D. Suvorov, Families of Planar Topological Mappings [in Russian], Nauka, Novosibirsk (1965).Google Scholar
  8. 8.
    V. P. Luferenko, “An analog of Caratheodory's theorem for families of homeomorphisms of regions,” in: Metric Problems in the Theory of Functions and Mappings [in Russian], Vol. 1, Naukova Dumka, Kiev (1969), pp. 120–139.Google Scholar
  9. 9.
    M. A. Lavrent'ev, “Stability in Liouville's theorem,” Dokl. Akad. Nauk SSSR,95, No. 5, 925–926 (1954).Google Scholar
  10. 10.
    P. P. Belinskii, “Stability in Liouville's theorem in spatial conformal mappings,” in: Some Problems in Mathematics and Mechanics, for M. A. Lavrent'ev's 70th Birthday [in Russian], Nauka, Leningrad (1971), pp. 88–101.Google Scholar
  11. 11.
    P. P. Belinskii, “The order of closeness of spatially quasiconformal mapping to a conformal mapping,” Sib. Mat. Zh.,14, No. 3, 475–483 (1973).Google Scholar
  12. 12.
    Yu. G. Reshetnyak, “Stability in Liouville's theorem on conformal mappings,” in: Some Problems in Mathematics and Mechanics, for M. A. Lavrent'ev's 60th Birthday [in Russian], Izd. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1961), pp. 219–223.Google Scholar
  13. 13.
    Yu. G. Reshetnyak, “Stability in Liouville's theorem on conformal mappings of regions with a nonsmooth boundary,” Sib. Mat. Zh.,17, No. 2, 361–369 (1976).Google Scholar
  14. 14.
    Yu. G. Reshetnyak, “Regions with the property of stability of Liouville's theorem on conformal spatial mappings,” in: Some Problems in Contemporary Function Theory. Matters of the Conference [in Russian], Izd. Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1976), pp. 185–187.Google Scholar
  15. 15.
    K. Kuratowski, Topology, Vol. 1, Academic Press (1966).Google Scholar
  16. 16.
    K. Kuratowski, Topology, Vol. 2, Academic Press (1969).Google Scholar
  17. 17.
    F. W. Gehring, “Quasiconformal mappings,” in: Complex Analysis and Its Applications, Lectures Int. Sem. Course, Trieste, Vol. 2, Vienna (1976), pp. 213–268.Google Scholar
  18. 18.
    A. V. Sychev, Spatial Quasiconformal Mappings [in Russian], Novosibirsk Univ. (1975).Google Scholar
  19. 19.
    P. M. Tamrazov, “The continuity of certain conformal invariants,” Ukr. Mat. Zh.,18, No. 6, 78–84 (1966).Google Scholar
  20. 20.
    V. A. Zorich, “Certain open problems in the theory of spatial quasiconformal mappings,” in: Metric Problems in the Theory of Functions and Mappings [in Russian], Vol. 3, Naukova Dumka, Kiev (1971), pp. 46–50.Google Scholar
  21. 21.
    P. Caraman, “Characterization of quasiconformality by arc families of extremal length zero,” Ann. Acad Sci. Fenn., Ser. AI,528, 1–10 (1973).Google Scholar

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© Plenum Publishing Corporation 1984

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  • V. V. Aseev

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