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Siberian Mathematical Journal

, Volume 28, Issue 6, pp 946–959 | Cite as

Estimates of stability for spatial quasiconformal mappings of a starlike region

  • V. I. Semenov
Article
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Keywords

Quasiconformal Mapping Spatial Quasiconformal Mapping 
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Literature Cited

  1. 1.
    M. A. Lavrent'ev, “On stability in Liouville's theorem,” Dokl. Akad. Nauk SSSR,95, No. 5, 925–926 (1954).Google Scholar
  2. 2.
    P. P. Belinskii, “Stability in the Liouville theorem on spatial quasiconformal mappings,” Some Problems of Mathematics and Mechanics [in Russian], pp. 88–101, Nauka, Leningrad (1970).Google Scholar
  3. 3.
    P. P. Belinskii, “On the order of closeness of a spatial quasiconformal mapping to the conformal one,” Sib. Mat. Zh.,14, No. 3, 475–483 (1973).Google Scholar
  4. 4.
    Yu. G. Reshetnyak, Stability Theorems in Geometry and Analysis [in Russian], Nauka, Novosibirsk (1982).Google Scholar
  5. 5.
    M. A. Lavrent'ev and P. P. Belinskii, “Some problems of geometric theory of functions,” Tr. Mat. Inst. im. V. A. Steklova,128, 34–40 (1972).Google Scholar
  6. 6.
    Yu. G. Reshetnyak, “Stability estimates in the class WP1 in Liouville's conformal mapping theorem for a closed region,” Sib. Mat. Zh.,17, No. 6, 1382–1394 (1976).Google Scholar
  7. 7.
    Yu. G. Reshetnyak, “Estimates for some differential operators with a finite-dimensional kernel,” Sib. Mat. Zh.,17, No. 2, 414–428 (1970).Google Scholar
  8. 8.
    L. V. Ahlfors, “Quasiconformal deformations and mappings in Rn,” J. Anal. Math.,30, 391–413 (1976).Google Scholar
  9. 9.
    S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Leningrad State Univ. (1950).Google Scholar
  10. 10.
    Ju. Vaisala, “Lectures on n-dimensional quasiconformal mappings,” Lect. Notes Math.,229, Springer, Berlin etc. (1971).Google Scholar
  11. 11.
    V. M. Gol'dshtein, “On the behavior of mappings with bounded distortion when the distortion coefficient is close to one,” Sib. Mat. Zh.,12, No. 6, 1250–1258 (1971).Google Scholar
  12. 12.
    O. Martio, S. Rickman, and Ju. Vaisala, “Topological and metric properties of quasiregular mappings,” Ann. Acad. Sci. Fenn.,1, No. 488, 1–31 (1971).Google Scholar
  13. 13.
    D. A. Trotsenko, “Continuation from a domain and approximation of spatial quasiconformal mappings with a small distortion coefficient,” Dokl. Akad. Nauk SSSR,270, No. 6, 1331–1333 (1983).Google Scholar
  14. 14.
    V. I. Semenov, “Uniform estimates of stability of isometries,” Sib. Mat. Zh.,27, No. 3, 193–199 (1986).Google Scholar
  15. 15.
    F. John, “Rotation and strain,” Commun. Pure Appl. Math.,14, 391–413 (1961).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • V. I. Semenov

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