Geodesic
Extremal problems on classes of quasi-conformal homeomorphisms
Sbornik. Mathematics, Tome 34 (1978) no. 1, pp. 99-109 
E. V. Sallinen. Extremal problems on classes of quasi-conformal homeomorphisms. Sbornik. Mathematics, Tome 34 (1978) no. 1, pp. 99-109. http://geodesic.mathdoc.fr/item/SM_1978_34_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This work is devoted to obtaining necessary conditions for the extremum of an arbitrary smooth functional on sets of quasi-conformal homeomorphisms of one finite Riemann surface onto another, in terms of its differential. Bibliography: 10 titles.

[1] H. Grotsch, “Über einige Extremalprobleme der konformen Abbildung. I, II”, Ber. Verh. Söchs. Akad. Wiss. Leipzig, 80 (1928), 367–376, 497–502

[2] O. Teichmuller, “Extremale quasikonforme Abbildungen und quadratishe Differentiable”, Abh. Preuss. Akad. Wiss., Math. Naturw. K1, 1940, no. 22, 3–197 | MR

[3] P. P. Belinskii, “O reshenii ekstremalnykh zadach teorii kvazikonformnykh otobrazhenii metodom variatsii”, DAN SSSR, 121:2 (1958), 199–201 | MR | Zbl

[4] P. P. Belinskii, “Reshenie ekstremalnykh zadach teorii kvazikonformnykh otobrazhenii variatsionnym metodom”, Sib. matem. zh., 1:3 (1960), 303–330 | MR | Zbl

[5] S. L. Krushkal, Kvazikonformnye otobrazheniya i rimanovy poverkhnosti, izd-vo “Nauka”, Novosibirsk, 1975 | MR | Zbl

[6] N. Burbaki, Differentsiruemye i analiticheskie mnogoobraziya, izd-vo “Mir”, Moskva, 1975 | MR

[7] I. N. Vekua, Obobschennye analiticheskie funktsii, Fizmatgiz, Moskva, 1959 | MR

[8] K. Iosida, Funktsionalnyi analiz, izd-vo “Mir”, Moskva, 1967 | MR

[9] L. V. Ahlfors, L. Bers, “Riemann's mapping theorem for variable metrics”, Ann. Math., 72 (1960), 358–404 | DOI | MR

[10] L. Bers, “A non-standart integral equation with application to quasiconformal mappings”, Acta math., 116 (1966), 113–134 | DOI | MR | Zbl