Abstract
The open questions of the theory of quasiconformal mappings that are adjacent to the field of studies of Professor Bogdan Bojarski are discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. V. Ahlfors, “Conformality with respect to Riemanian metrics,” Ann. Acad. Sci. Fenn. Ser. A. I., No. 206, 1–22 (1955).
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).
B. V. Bojarski, “Homeomorphic solutions of Beltrami systems,” Dokl. Akad. Nauk SSSR, 102, No. 4, 661–664 (1955).
I. N. Vekua, Generalized Analytic Functions, Pergamon Press, New York, 1962.
L. Ahlfors and L. Bers, “Riemann’s mapping theorem for variable metrics,” Ann. Math., Ser. 2, 72, No. 2, 385–404 (1960).
L. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, New York, 1966.
B. Bojarski and T. Iwaniec, “Analytical foundations of the theory of quasiconformal mappings,” Annales Acad. Sci. Fenn., 257–324 (1982).
T. Iwaniec and G. Martin, Geometric Functional Theory and Nonlinear Analysis, Oxford Univ. Press, Oxford, 2001.
T. Iwaniec and G. Martin, The Beltrami Equation, Amer. Math. Soc., Providence, RI, 2008.
R. Nevanlinna, “On differentiable mappings,” Princeton Math. Ser., 90, No. 4, 571–574 (1984).
M. Gromov, https://www.ihes.fr/ gromov/wp-content/uploads/2018/08/problems-sept2014-copy.pdf
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).
F. John, “On quasi-isometric mappings, II,” Comm. Pure Appl. Math., 22, 41–66 (1969).
V. A. Zorich, “Some remarks on multidimensional quasiconformal mappings,” Matem. Sbor., 208, No. 3, 72–95 (2017).
V. A. Zorich, “Quasiconformal mappings and asymptotic geometry of manifolds,” Uspekhi Mat. Nauk, 57, No. 3 (345), 3–28 (2002).
V. A. Zorich, “To the problem of isotopy of a quasiconformal mapping,” Trudy Mat. Inst. im. V. A. Steklova, 298, 139–143 (2017).
Author information
Authors and Affiliations
Corresponding author
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
About this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-019-04520-6