Skip to main content
Log in

K-Capacity and the rado problem for mappings with bounded distortion

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. R. Kaufman, “A theorem of Rado,” Math. Ann.,169, 282 (1967).

    Google Scholar 

  2. R. Kaufman, “Null sets and analytic continuation,” Math. Ann.,260, 63–65 (1982).

    Google Scholar 

  3. P. Järvi, “Removability theorems for meromorphic functions,” Ann. Acad. Sci. Fenn. Ser. Al, No. 12, 1–33 (1977).

    Google Scholar 

  4. L. Ahlfors and A. Beurling, “Conformal invariants and function-theoretic null-sets,” Acta Math.,83, 101–129 (1950).

    Google Scholar 

  5. A. V. Sychev, Moduli and Spatial Mappings [in Russian], Nauka, Novosibirsk (1983).

    Google Scholar 

  6. Yu. G. Reshetnyak, Spatial Mappings with Bounded Distortion [in Russian], Nauka, Novosibirsk (1982).

    Google Scholar 

  7. V. M. Gol'dshtein and Yu. G. Reshetnyak, An Introduction to the Theory of Functions with Generalized Derivatives and Quasiconformal Mappings [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  8. W. P. Ziemer, “Extremal length and conformal capacity,” Trans. Am. Math. Soc.,126, No. 3, 460–473 (1967).

    Google Scholar 

  9. E. Riech and S. E. Warschawski, “On canonical conformal maps of regions of arbitrary connectivity,” Pacif. J. Math.,10, No. 3, 965–989 (1960).

    Google Scholar 

  10. K. Kuratowskii, Topology, Academic Press, New York (1966–68).

    Google Scholar 

  11. G. D. Mostow, “Quasiconformal mappings in n-dimensional space and the rigidity of hyperbolic space forms,” Inst. Hautes Études Sci. Publ. Math. No.34, 53–104 (1968).

    Google Scholar 

  12. L. I. Hedberg, “Removable singularities and condenser capacities,” Ark. Mat.,13, No. 1, 131–144 (1975).

    Google Scholar 

  13. V. V. Krivov, “The method of extremal functions in the theory of quasiconformal mappings,” Sib. Mat. Zh.,12, 1056–1066 (1971).

    Google Scholar 

  14. P. S. Aleksandrov, Introduction to Set Theory and General Topology [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  15. G. V. Vittikh, A Recent Investigation into Single-Valued Analytic Functions [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

  16. O. Martio, S. Rickman, and J. Väisälä, “Definitions for quasiregular mappings,” Ann. Acad. Sci. Fenn. Ser. Al, No. 448, 1–40 (1969).

    Google Scholar 

Download references

Authors

Additional information

Vladivostok. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 179–186, January–February, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shlyk, V.A. K-Capacity and the rado problem for mappings with bounded distortion. Sib Math J 31, 152–158 (1990). https://doi.org/10.1007/BF00971161

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00971161

Navigation