Literature Cited
S. L. Krushkal', Quasiconformal Mappings and Riemann Surfaces [in Russian], Nauka, Novosibirsk (1975).
R. S. Hamilton, “Extremal quasiconformal mappings with prescribed boundary values,” Trans. Am. Math. Soc.,138, 399–406 (1969).
E. Reich and K. Strebel, “Extremal plane quasiconformal mappings with given boundary values,” Bull. Am. Math. Soc.,79, 488–490 (1973).
V. G. Sheretov, “On the theory of extremal quasiconformal mappings,” Mat. Sb.,107, No. 1, 146–158 (1978).
V. G. Sheretov, “Criteria for extremality in a problem for quasiconformal mappings,” Mat. Zametki,39, No. 1, 14–23 (1986).
C. W. Misner, “Harmonic maps as models for physical theories,” Phys. Rev. D,18, No. 12, 4510–4524 (1978).
M. Forger, “Instantons in nonlinear σ-models, gauge theories and general relativity,” in: Differential Geometric Methods in Mathematical Physics, Lect. Notes in Phys.,139, Springer, Berlin (1981), pp. 110–134.
J.-P. Bourguignon, “Harmonic curvature for gravitational and Yang-Mills fields,” in: Harmonic Maps, Lect. Notes in Math.,949, Springer, Berlin (1982), pp. 35–47.
J. Jost, Harmonic Maps between Surfaces, Lect. Notes in Math.,1062, Springer, Berlin (1984).
L. Bers, On Moduli of Riemann Surfaces, Forschungsinstitut für Math., Zürich (1964).
V. G. Sheretov, “On extremal quasiconformal mappings with bounded characteristics,” Dokl. Akad. Nauk SSSR,179, No. 5, 1060–1063 (1968).
G. D. Suvorov, The Metric Theory of Prime Ends and Boundary Properties of Plane Mappings with Bounded Dirichlet Integrals, Naukova Dumka, Kiev (1981).
L. Ahlfors and L. Lars, The Spaces of Riemann Surfaces and Quasiconformal Mappings [Russian translation], IL, Moscow (1961).
R. S. Hamilton, Harmonic Maps of Manifolds with Boundary, Lect. Notes in Math.,471, Springer, Berlin etc. (1975).
J. Lelong-Ferrand, “Constructions de modules de continuite dans le case limite de Soboleff et applications a la geometrie differentielle,” Arch. Ration. Mech. Anal.,52, No. 4, 297–311 (1973).
V. G. Sheretov, “The Dirichlet principle and extremal quasiconformal mappings of open Riemann surfaces,” Dokl. Akad. Nauk SSSR,219, No. 3, 558–560 (1974).
V. G. Sheretov, “On extremal quasiconformal mappings with given boundary correspondence,” Sib. Mat. Zh.,19, No. 4, 942–952 (1978).
V. G. Sheretov, “Quasiconformal mappings extremal with respect to their boundary values,” Sib. Mat. Zh.,27, No. 4, 161–166 (1986).
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Equations of Elliptic Type, Pergamon (1970).
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Krasnodar. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 3, pp. 163–174, May–June, 1988.
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Sheretov, V.G. Quasiconformal extremals of smooth functionals and of the energy integral on Riemann surfaces. Sib Math J 29, 467–476 (1988). https://doi.org/10.1007/BF00969658
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DOI: https://doi.org/10.1007/BF00969658