This is a preview of subscription content, log in via an institution to check access.
References
L. V. Ahlfors, “On quasiconformal mappings,” J. Analyse Math.,3, 1–58 (1953–1954).
P. A. Biluta, “Some extremal problems for mean quasiconformal mappings,” Sibirsk. Mat. Zh.,6, No. 4, 717–726 (1965).
V. I. Kruglikov and V. M. Miklyukov, “On some classes of plane topological mappings with weak derivatives,” in: Metric Questions of the Theory of Functions and Mappings [in Russian], Naukova Dumka, Kiev, 1973, pp. 102–122.
V. I. Kruglikov, “On existence and uniqueness of mean quasiconformal mappings,” in: Metric Questions of the Theory of Functions and Mappings [in Russian], Naukova Dumka, Kiev, 1973, pp. 123–147.
S. L. Krushkal' and R. Kühnau, Quasiconformal Mappings: New Methods and Applications [in Russian], Nauka, Novosibirsk (1984).
M. Perovich, “Global homeomorphy of mean quasiconformal mappings,” Dokl. Akad. Nauk SSSR,230, No. 4, 781–784 (1976).
I. N. Pesin, “Mean quasiconformal mappings,” Dokl. Akad. Nauk SSSR,187, No. 4, 740–742 (1969).
V. M. Miklyukov and G. D. Suvorov, “On existence and uniqueness of quasiconformal mappings with unbounded characteristics,” in: Studies on the Theory of Functions of Complex Variables and Its Applications [in Russian], Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev, 1972, pp. 45–53.
G. R. David, “Solutions de l'equation de Beltrami avec ∥Μ∥∞=1,” Ann. Acad. Sci. Fenn. Ser. A I. Math.,13, No. 1, 25–70 (1988).
P. Tukia, “Compactness properties ofΜ-homeomorphisms,” Ann. Acad. Sci. Fenn. Ser. A I. Math.,16, No. 1, 47–69 (1991).
V. I. Ryazanov, “Some questions of convergence and compactness for quasiconformal mappings,” Amer. Math. Soc. Transl. Ser. 2,131, No. 2, 7–19 (1986).
V. Ya. Gutlyanskii and V. I. Ryazanov, “On quasiconformal mappings with integral constraints on the Lavrent'ev characteristic,” Sibirsk. Mat. Zh.,31, No. 2, 21–36 (1990).
V. I. Ryazanov, “On compactification of classes with integral constraints on the Lavrent'ev characteristic,” Sibirsk. Mat. Zh.,33, No. 1, 87–104 (1992).
V. I. Ryazanov, “On quasiconformal mappings with constraints on measure,” Ukrain. Mat. Zh.,45, No. 7, 1009–1019 (1993).
F. M. Gehring and O. Lehto, “On the differentiability of functions of a complex variable,” Ann. Acad. Sci. Fenn. Ser. A I. Math.,272, 1009–1019 (1959).
L. Ahlfors, Lectures on Quasiconformal Mappings [Russian translation], Mir, Moscow (1969).
V. Ya. Gutlyanskii, “On the variational method for univalent functions with quasiconformal extension,” Sibirsk. Mat. Zh.,21, No. 2, 61–78 (1980).
O. Lehto and K. I. Virtanen, Quasikonforme Abbildungen, Springer, Berlin-New York (1965).
S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Vysshaya Shkola, Moscow (1977).
N. Bourbaki, Functions of a Real Variable. Elementary Theory [Russian translation], Nauka, Moscow (1965).
N. Dunford and J. T. Schwartz, Linear Operators. Vol. 1: General Theory [Russian translation], Izdat. Inostr. Lit., Moscow (1962).
G. M. Goluzin, Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).
K. Kuratowski, Topology. Vol. 1 [Russian translation], Mir, Moscow (1966).
K. Kuratowski, Topology. Vol. 2 [Russian translation], Mir, Moscow (1969).
N. Bourbaki, General Topology. Fundamental Structures [Russian translation], Nauka, Moscow (1968).
S. Sacks, Theory of the Integral [Russian translation], Izdat. Inostr. Lit., Moscow (1949).
B. V. Bojarsky, “Weak solutions to a system of first-order differential equations of elliptic type with discontinuous coefficients,” Mat. Sb.,4, No. 4, 451–503 (1957).
Author information
Authors and Affiliations
Additional information
The research was partly supported by the International Science Foundation (Grant U 96 000).
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 37, No. 2, pp. 378–388, March–April, 1996.
Rights and permissions
About this article
Cite this article
Ryazanov, V.I. On mean quasiconformal mappings. Sib Math J 37, 325–334 (1996). https://doi.org/10.1007/BF02104876
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02104876