Literature Cited
P. P. Belinskii, General Properties of Quasiconformal Mappings [in Russian], Nauka, Novosibirsk (1974).
S. L. Krushkal' Quansiconformal Mappings and Riemann Surfaces [in Russian], Nauka Novosibirsk (1975).
P. A. Biluta, “On the solution of extremal problems for a class of quasiconformal mappings,” Sib. Mat. Zh.,10, No. 4 734–743 (1969).
V. Ya. Gutlyanskii and V. I. Ryazanov, “On the variational method for quasiconformal mappings,” Sib. Mat. Zh.,28, No. 1, 81–85 (1987).
V. G. Sheretov, “A criterion for extremality in a problem for quasiconformal mappings,” Mat. Zametki,39, No. 1, 27–36 (1986).
E. V. Sallinen, “Extremal problems on classes of quasiconformal mappings,” Mat. Sb.,105, No. 1, 109–120 (1978).
S. L. Krushkal' and R. Kühnau, Quasiconformal Mappings—New Methods and Applications [in Russian], Nauka, Novosibirsk (1984).
I. Kra, “The Carathéodory metric on Abelian Teichmüller disks,” J. Anal. Math.,40, 129–143 (1981).
S. L. Krushkal', “Invariant metrics on spaces of closed Riemann surfaces,” Sib. Mat. Zh.,26, No. 2, 108–114 (1985).
H. L. Royden, “Automorphisms and isometries of Teichmüller space,” in: Advances in the Theory of Riemann Surfaces, Princeton Univ. Press (1971), pp. 369–383.
F. P. Gardiner, “Approximation on infinite-dimensional Teichmüller spaces,” Trans. Am. Math. Soc.,282, No. 1, 367–383 (1984).
S. L. Krushkal', “A new approach to variational problems in the theory of quasiconformal mappings,” Dokl. Akad. Nauk SSSR,292, No. 6, 1297–1300 (1987).
C. J. Earle and I. Kra, “On sections of some holomorphic families of closed Riemann surfaces,” Acta Math.,137, Nos. 1–2, 49–79 (1976).
R. S. Hamilton, “Extremal quasiconformal mappings with prescribed boundary values,” Trans. Am. Math. Soc.,138, 399–406 (1969).
C. J. Earle, “On holomorphic cross sections in Teichmüller spaces,” Duke Math. J.,36, No. 2, 409–415 (1969).
L. V. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, Toronto-New York-London (1966).
S. L. Krushkal', “On the coefficient problem for univalent functions with a quasiconformal continuation,” Dokl. Akad. Nauk SSSR,287, No. 3, 547–550 (1986).
Additional information
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 2, pp. 105–114, March–April, 1988.
Rights and permissions
About this article
Cite this article
Krushkal', S.L. A new method of solving variational problems in the theory of quasiconformal mappings. Sib Math J 29, 245–252 (1988). https://doi.org/10.1007/BF00969736
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969736