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On boundary values of quasiconformal mappings in space

  • I Section Quasiconformal And Quasiregular Mappings. Teichmüller Spaces And Kleinian Groups
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  • First Online:
Romanian-Finnish Seminar on Complex Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 743))

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Quoted bibliography

  1. Beurling A, Ahlfors L.V., The boundary correspondence under quasiconformal mapping, Acta math., 1956, 96, 125–142.

    Article  MathSciNet  MATH  Google Scholar 

  2. Ahlfors L.V., Beurling A., Conformal invariants and function-theoretic null-sets, Acta Math., 1950, 83, 101–129.

    Article  MathSciNet  MATH  Google Scholar 

  3. Belinskii P.P., On the continuity of the quasiconformal mappings in space and on Liouville’s theorem (Russian), Dokl.Akad.Nauk SSSR, 1962, 147, 1003–1004.

    MathSciNet  Google Scholar 

  4. Belinskii P.P., Stability in Liouville’s theorem on quasiconformal mappings in space (Russian), in the volume "Nekotorye problemy mat. i meh.,” Nauka, Leningrad, 1970, p.88–102.

    Google Scholar 

  5. Belinskii P.P., On the degree of closeness of the quasiconformal mappings in the space to the conformal ones (Russian), Dokl.Akad.Nauk SSSR, 1971, 200, 759–761.

    MathSciNet  Google Scholar 

  6. Kopylov A.P., On the behaviour on hyperplanes of spatially quasiconformal close to conformal mappings (Russian), Dokl.Akad.Nauk SSSR, 1973, 209, 1278–1280.

    MathSciNet  Google Scholar 

  7. Kopylov A.P., Behaviour of spatially quasiconformal mappings on plane sections of the domain of definition (Russian), Dokl.Akad.Nauk SSSR, 1966, 167, 743–746.

    MathSciNet  Google Scholar 

  8. Ahlfors L.V., Extension of quasiconformal mappings from two to three dimensions, Proc.Nat.Acad.Sci. USA, 1964,51, 768–771.

    Article  MathSciNet  MATH  Google Scholar 

  9. Carleson L., The Extension Problem for Quasiconformal Mappings, A Collection of Papers Dedicated to Lipman Bers "Contribution to Analysis", Academic Press New York and London, 1974, pp.39–47.

    Google Scholar 

  10. Gol’dstein V.M., Approximation of quasiconformal homeomorphisms by simplicial quasiconformal homeomorphisms (Russian), Dokl.Akad.Nauk SSSR, 1973, 213, 23–25.

    MathSciNet  Google Scholar 

  11. Sedo R.I., Sycev A.V., On the extension of quasiconformal mappings to multidimensional spaces in higher dimension (Russian), Dokl.Akad.Nauk SSSR, 1971, 198, 1278–1279.

    MathSciNet  Google Scholar 

  12. Vaisälä J., On quasiconformal mappings in space, Ann.Acad.Sci.Fenn., Ser AI, 1961, 298.

    Google Scholar 

  13. Resetnjak Ju.G, Stability in Liouville’s theorem on conformal mappings in space (Russian), in the volume "Nekotorye problemy mat. i meh.", Novosibirsk, 1961, p.219–223.

    Google Scholar 

  14. Resetnjak Ju.G., On the stability in Liouville’s theorem on conformal mappings in space (Russian), Dokl.Akad.Nauk SSSR, 1963, 152, 286–287.

    MathSciNet  Google Scholar 

  15. Sobolev S.L., Some applications of functional analysis to mathematical physics (Russian), Novosibirsk, 1962.

    Google Scholar 

  16. Kopylov A.P., On the approximation of spatially quasiconformal, close to conformal mappings, by smooth quasiconformal mappings (Russian), Sibirsk Mat.Ž. 1972, 13, 94–106.

    MathSciNet  Google Scholar 

  17. Vodop’janov C.K., Gol’dstein V.M., Quasiconformal mappings and spaces of functions with first generalized derivatives (Russian) Sibirsk. Mat. Ž., 1976, 17, nr. 3, 515–531.

    MathSciNet  Google Scholar 

  18. Vodop’janov C.K., Gol’dctein V.K., Structural isomorphisms of the spaces W1 n and quasiconformal mappings (Russian), Sibirsk. Mat. Ž, 1975, 16, nr.2, 224–246.

    MathSciNet  Google Scholar 

  19. Vodop’janov C.K., Gol’dstein V.M., Removability of the sets for the spaces W1 p of quasiconformal and quasi-isometric mappings (Russian), Dokl.Akad.Nauk. SSSR, 1975, 220, nr.4, 769–771.

    MathSciNet  Google Scholar 

  20. Hesse J., A p-extremal length and p-capacity.Arkiv.mat., 1975, 13, 131–144.

    Article  MathSciNet  MATH  Google Scholar 

  21. Väisälä J., On null-sets for extremal length. Ann.Acad.Sci.Fenn. Ser AI, 1962, 322.

    Google Scholar 

  22. Pesin I.N., Metric properties of Q-quasiconformal mappings (Russian), Mat.Sb., 1956, 40(82), nr.3, 281–294.

    MathSciNet  MATH  Google Scholar 

  23. Aseev V.V., Syčev A.V., On the removable sets for spatially quasiconformal mappings (Russian), Sibirsk. Mat.Ž., 15, nr.6,1974, 1213–1227.

    MathSciNet  Google Scholar 

  24. Zorič V.A., Boundary correspondence under Q-quasiconformal mappings of the ball (Russian). Dokl.Akad.Nauk SSSR, 1962, 145, Nr.6, 1209–1212.

    MathSciNet  Google Scholar 

  25. Zorič V.A., Definition of boundary elements by means of sections (Russian), Dokl. Akad.Nauk SSSR, 1965, 164,Nr.4, 736–739.

    MathSciNet  Google Scholar 

  26. Gehring F.W., Väisälä Ju., The coefficients of quasiconformality of domains in space, Acta Math., 1965, 114, 1–70 (Russian translation in Mathematika, Sb.per., 1966, 10, Nr.6, 60–120).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut Matematiki SO AN SSSR Novosobirsk, USSR

    S. K. Vodop’ianov, V. M. Gol’dstein & A. P. Kopylov

Authors
  1. S. K. Vodop’ianov
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  2. V. M. Gol’dstein
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  3. A. P. Kopylov
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Cabiria Andreian Cazacu Aurel Cornea Martin Jurchescu Ion Suciu

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© 1979 Springer-Verlag

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Vodop’ianov, S.K., Gol’dstein, V.M., Kopylov, A.P. (1979). On boundary values of quasiconformal mappings in space. In: Cazacu, C.A., Cornea, A., Jurchescu, M., Suciu, I. (eds) Romanian-Finnish Seminar on Complex Analysis. Lecture Notes in Mathematics, vol 743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079497

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  • DOI: https://doi.org/10.1007/BFb0079497

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09550-7

  • Online ISBN: 978-3-540-34861-0

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