Siberian Mathematical Journal

, Volume 11, Issue 5, pp 744–750 | Cite as

A homotopic property of mappings with bounded distortion

  • V. M. Gol'dshtein


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    S. T. Hu, Homotopy Theory [Russian translation], Mir (1964).Google Scholar
  2. 2.
    Yu. G. Reshtnyak, “Estimates of the modulus of continuity for certain mappings,” Sibirsk. Matem. Zh.,7, No. 5, 1106–1114 (1966).Google Scholar
  3. 3.
    Yu. G. Reshetnyak, “Space mappings with bounded distortion,” Sibirsk. Matem. Zh.,8, No. 3, 629–658 (1967).Google Scholar
  4. 4.
    M. A. Lavrent'ev, “On one differential indication of the homeomorphism of mappings of three-dimensional regions,” Dokl. Akad. Nauk SSSR,20, No. 4, 241–242 (1938).Google Scholar
  5. 5.
    V. A. Zorich, “M. A. Lavrent'ev's theorem on quasiconformal mappings in space,” Matem. Sb.,74, No. 3, 417–433 (1967).Google Scholar
  6. 6.
    L. V. Ahlfors and A. Beurling, “Conformal invariants and function-theoretic null sets” Acta Math.,83, 101–121 (1950).Google Scholar
  7. 7.
    L. Fuglede, “Extremal length and functional completion,” Acta Math.,98, 171–219 (1957).Google Scholar
  8. 8.
    B. V. Shabat, “Modulus method in space,” Dokl. Akad. Nauk SSSR,130, No. 6, 1210–1213 (1969).Google Scholar
  9. 9.
    F. W. Ghering and J. Väisäilä, “The coefficient of quasiconformality of domains in space,” Acta Math.,114, 1–70 (1965).Google Scholar
  10. 10.
    S. Saks, Theory of the Integral, Dover Publications, New York (1964).Google Scholar
  11. 11.
    Yu. G. Reshetnyak, “Local structure of mappings with bounded distortion,” Sibirsk. Matem. Zh.,10, No. 6, 1311–1353 (1969).Google Scholar
  12. 12.
    J. Väisäilä, “On quasiconformal mapping in space,” Ann. Acad. Sci. Fenn., Ser. AI,298, 1–36 (1964).Google Scholar
  13. 13.
    J. Väisäilä, “Removable sets for quasiconformal mapping,” J. Math. and Mech.,19, No. 1, 49–51 (1969).Google Scholar
  14. 14.
    P. T. Church and E. Hemmingsen, “Light open sets in n-manifolds,” Duke Math. J.,27, No. 4, 527–536 (1960).Google Scholar
  15. 15.
    G. Th. Whyburn, Analytic Topology, Amer. Math. Soc., Providence, R. I. (1942).Google Scholar

Copyright information

© Consultants Bureau 1971

Authors and Affiliations

  • V. M. Gol'dshtein

There are no affiliations available

Personalised recommendations