Skip to main content
Log in

To the theory of quasiconformal mappings

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The open questions of the theory of quasiconformal mappings that are adjacent to the field of studies of Professor Bogdan Bojarski are discussed.

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.

Similar content being viewed by others

References

  1. L. V. Ahlfors, “Conformality with respect to Riemanian metrics,” Ann. Acad. Sci. Fenn. Ser. A. I., No. 206, 1–22 (1955).

  2. I. N. Vekua, “The problem of reduction of differential forms of the elliptic type to the canonical form and the generalized Cauchy–Riemann system,” Dokl. Akad. Nauk SSSR, 100, No. 2, 197–200 (1955).

    MathSciNet  Google Scholar 

  3. B. V. Bojarski, “Homeomorphic solutions of Beltrami systems,” Dokl. Akad. Nauk SSSR, 102, No. 4, 661–664 (1955).

    MathSciNet  Google Scholar 

  4. I. N. Vekua, Generalized Analytic Functions, Pergamon Press, New York, 1962.

  5. L. Ahlfors and L. Bers, “Riemann’s mapping theorem for variable metrics,” Ann. Math., Ser. 2, 72, No. 2, 385–404 (1960).

    Article  MathSciNet  Google Scholar 

  6. L. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, New York, 1966.

  7. B. Bojarski and T. Iwaniec, “Analytical foundations of the theory of quasiconformal mappings,” Annales Acad. Sci. Fenn., 257–324 (1982).

  8. T. Iwaniec and G. Martin, Geometric Functional Theory and Nonlinear Analysis, Oxford Univ. Press, Oxford, 2001.

  9. T. Iwaniec and G. Martin, The Beltrami Equation, Amer. Math. Soc., Providence, RI, 2008.

  10. R. Nevanlinna, “On differentiable mappings,” Princeton Math. Ser., 90, No. 4, 571–574 (1984).

    Google Scholar 

  11. M. Gromov, https://www.ihes.fr/ gromov/wp-content/uploads/2018/08/problems-sept2014-copy.pdf

  12. O. Martio, S. Rickman, and J. Väisälä, “Topological and metric properties of quasiregular mappings,” Ann. Acad. Sci. Fenn. Ser. A. I., Math., 488, 1–31 (1971).

    MathSciNet  MATH  Google Scholar 

  13. F. John, “On quasi-isometric mappings, II,” Comm. Pure Appl. Math., 22, 41–66 (1969).

    Article  MathSciNet  Google Scholar 

  14. V. A. Zorich, “Some remarks on multidimensional quasiconformal mappings,” Matem. Sbor., 208, No. 3, 72–95 (2017).

    Google Scholar 

  15. V. A. Zorich, “Quasiconformal mappings and asymptotic geometry of manifolds,” Uspekhi Mat. Nauk, 57, No. 3 (345), 3–28 (2002).

  16. V. A. Zorich, “To the problem of isotopy of a quasiconformal mapping,” Trudy Mat. Inst. im. V. A. Steklova, 298, 139–143 (2017).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vladimir A. Zorich.

Additional information

The article is dedicated to the memory of Professor Bogdan Bojarski

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 1, pp. 141–147 January–March, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zorich, V.A. To the theory of quasiconformal mappings. J Math Sci 242, 860–864 (2019). https://doi.org/10.1007/s10958-019-04520-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-019-04520-6

Keywords

Navigation