Geodesic
On the theory of extremal quasiconformal mappings
Sbornik. Mathematics, Tome 35 (1979) no. 3, pp. 437-447
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this work criteria are established for the extremality of both quasiconformal deformations of open Riemann surfaces of hyperbolic type and Kleinian groups of the mappings in homotopy classes modulo ideal boundaries. The existence of generalized harmonic quasiconformal mappings in these classes is shown. Bibliography: 17 titles. 
@article{SM_1979_35_3_a7,
     author = {V. G. Sheretov},
     title = {On the theory of extremal quasiconformal mappings},
     journal = {Sbornik. Mathematics},
     pages = {437--447},
     year = {1979},
     volume = {35},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_3_a7/}
}
TY  - JOUR
AU  - V. G. Sheretov
TI  - On the theory of extremal quasiconformal mappings
JO  - Sbornik. Mathematics
PY  - 1979
SP  - 437
EP  - 447
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1979_35_3_a7/
LA  - en
ID  - SM_1979_35_3_a7
ER  - 
%0 Journal Article
%A V. G. Sheretov
%T On the theory of extremal quasiconformal mappings
%J Sbornik. Mathematics
%D 1979
%P 437-447
%V 35
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1979_35_3_a7/
%G en
%F SM_1979_35_3_a7
V. G. Sheretov. On the theory of extremal quasiconformal mappings. Sbornik. Mathematics, Tome 35 (1979) no. 3, pp. 437-447. http://geodesic.mathdoc.fr/item/SM_1979_35_3_a7/

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

[2] S. L. Krushkal, “K teorii ekstremalnykh kvazikonformnykh otobrazhenii”, Sib. matem. zh., 10:3 (1969), 573–583 | MR | Zbl

[3] R. S. Hamilton, “Extremal quasiconformal mappings with prescribed boundary values”, Trans. Amer. Math. Soc,, 138 (1969), 399–406 | DOI | MR | Zbl

[4] L. Bers, “Extremal quasiconformal mappings”, Ann. Math. Stud., 1972, no. 66, 27–52 | MR

[5] E. Reich, K. Strebel, Contributions to Analyse, New York–London, 1974, 375–391 | MR | Zbl

[6] K. Strebel, “Zur Frage der Eindeutigkeit extremaler quasikonforme Abbildung des Einheitkreises. I; II”, Comm. Math. Helv., 36:4 (1962) ; 39:1–2 (1964), 77–89 | MR | Zbl | DOI | MR | Zbl

[7] L. Bers, “On moduli of Riemann surfaces”, Lectures at Forsch. für Math., Zürich, 1964

[8] L. Alfors, Lektsii po kvazikonformnym otobrazheniyam, izd-vo “Mir”, Moskva, 1969 | MR

[9] L. Alfors, L. Bers, Prostranstva rimanovykh poverkhnostei i kvazikonformnye otobrazheniya, IL, Moskva, 1961

[10] B. V. Shabat, Vvedenie v kompleksnyi analiz, t. 1, izd-vo “Nauka”, Moskva, 1976 | MR

[11] C. Earle, J. Eells, “On the differential geometry of Teichmuller spaces”, J. Analyse Math., 19 (1967), 35–52 | DOI | MR | Zbl

[12] I. Kra, Avtomorfnye formy i kleinovy gruppy, izd-vo “Mir”, Moskva, 1975 | MR

[13] K. Shibata, “On the existence of a harmonic mappings”, Osaca Math. J., 15 (1963), 173–211 | MR | Zbl

[14] V. G. Sheretov, “Funktsionaly tipa Dirikhle i garmonicheskie kvazikonformnye otobrazheniya”, DAN SSSR, 209:4 (1973), 808–810 | Zbl

[15] G. D. Suvorov, Semeistva ploskikh topologicheskikh otobrazhenii, izd. SO AN SSSR, Novosibirsk, 1965 | MR

[16] Brian O'Burne, “On Finstler geometry and applications to Teichmüller space”, Ann. Math. Stud., 1972, no. 66, 317–328

[17] O. Teichmuller, “Extremale quasikonforme Abbildungen und quadratische Differentiale”, Abh. Preuss. Akad. Wiss., Math-Naturwiss, KL:22 (1940), 3–197 | MR