Skip to main content
Log in

On sets which are removable for quasiconformal space mappings

  • 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. J. Väisälä, On quasiconformal mappings in space, Ann. Acad. Sci. Fenn., Ser. A.,298, 1–36 (1961).

    Google Scholar 

  2. L. Ahlfors, and A. Beurling, Conformal invariants and function theoretic null sets, Acta Math.,83, 100–129 (1950).

    Google Scholar 

  3. J. Väisälä, On null sets for extremal length, Ann. Acad. Sci. Fenn., Ser. A,322, 1–12 (1962).

    Google Scholar 

  4. V. V. Aseev, “Examples of NED-sets in n-dimensional Euclidean space which have positive (n-1)-dimensional Hausdorffmeasure,” Dokl. AN SSSR,216, No. 4, 717–720 (1974).

    Google Scholar 

  5. I. N. Pesin, “Metric properties of Q-quasiconformal mappings,” Matem. Sb.,40 (82), No. 3, 281–294 (1956).

    Google Scholar 

  6. B. V. Shabat, “On the theory of quasiconformal mappings in space,” Dokl. AN SSSR,132, No. 5, 1045–1048 (1960).

    Google Scholar 

  7. A. P. Kopylov and I. N. Pesin, “The removability of some sets in the class of three dimensional quasiconformal mappings,” Matem. Zametki,7, No. 6, 717–722 (1970).

    Google Scholar 

  8. A. P. Kopylov, “On the removability of plane sets in the class of three dimensional quasiconformal mappings,” in: Metric Questions of the Theory of Functions and Mappings [in Russian], Vol. 1, Kiev (1969), pp. 21–23.

  9. V. M. Miklyukov, “On removable singularities of quasiconformal mappings in space,” Dokl. AN SSSR,188, No. 3, 525–527 (1969).

    Google Scholar 

  10. J. Väisälä, Removable sets for quasiconformal mappings, J. Math, Mech.,19, No. 1, 49–51 (1969).

    Google Scholar 

  11. Yu. G. Reshetnyak, “On the concept of capacity in the theory of functions with generalized derivatives,” Sib. Matem. Zh.,10, No. 5, 1110–1138 (1969).

    Google Scholar 

  12. B. Fuglede, Extremal length and functional completion, Acta Math.,98, Nos. 3–4, 171–219 (1957).

    Google Scholar 

  13. H. Wallin, A connection between α-capacity and Lp-classes of differentiable functions, Arch. Math.,5, No. 4, 331–341 (1965).

    Google Scholar 

  14. H. Walling, Riesz potentials, k. p-capacity, and p-modules, Mich. Math. J., 18, No. 3, 257–263 (1971).

    Google Scholar 

  15. W. Ziemer, Extremal length as a capacity, Mich. Math. J.,17, No. 2, 117–128 (1970).

    Google Scholar 

  16. V. V. Aseev, “On a property of the module,” Dokl. AN SSSR,200, No. 3, 513–514 (1971).

    Google Scholar 

  17. K. Kuratovskii, Topology [in Russian], Vol. 1, “Mir,” Moscow (1966).

    Google Scholar 

  18. T. Rado and P. V. Reichelderfer, Continuous Transformations in Analysis, Springer, Berlin-Göttingen-Heidelberg (1955).

    Google Scholar 

  19. Yu. G. Reshetnyak, “Space mappings with bounded distortion,” Sib. Matem. Zh.,8, No. 3, 629–658 (1967).

    Google Scholar 

  20. R. Gehring, Extension theorems for quasiconformal mappings in space. J. Anal. Math.,19, 149–169 (1967).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 6, pp. 1213–1227, November–December, 1974.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aseev, V.V., Sychev, A.V. On sets which are removable for quasiconformal space mappings. Sib Math J 15, 851–861 (1974). https://doi.org/10.1007/BF00966553

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00966553

Keywords

Navigation