Geodesic
On the local behaviour of quasi-conformal mappings
Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 471-498.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to the study of the local behaviour of quasi-conformal mappings on the plane and related questions of boundary correspondence in dependence on properties of complex characteristics. The Gardiner–Sullivan symmetries are investigated as well as quasi-circles asymptotically conformal in the sense of Becker and Pommerenke. 
@article{IM2_1995_59_3_a1,
     author = {V. Ya. Gutlyanskii and V. I. Ryazanov},
     title = {On the local behaviour of quasi-conformal mappings},
     journal = {Izvestiya. Mathematics },
     pages = {471--498},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a1/}
}
TY  - JOUR
AU  - V. Ya. Gutlyanskii
AU  - V. I. Ryazanov
TI  - On the local behaviour of quasi-conformal mappings
JO  - Izvestiya. Mathematics 
PY  - 1995
SP  - 471
EP  - 498
VL  - 59
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a1/
LA  - en
ID  - IM2_1995_59_3_a1
ER  - 
%0 Journal Article
%A V. Ya. Gutlyanskii
%A V. I. Ryazanov
%T On the local behaviour of quasi-conformal mappings
%J Izvestiya. Mathematics 
%D 1995
%P 471-498
%V 59
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a1/
%G en
%F IM2_1995_59_3_a1
V. Ya. Gutlyanskii; V. I. Ryazanov. On the local behaviour of quasi-conformal mappings. Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 471-498. http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a1/

[1] Agard S. B., Gehring F. W., “Angles and quasiconformal mappings”, Proc. London Math. Soc., 3:14 A (1965), 1–21 | MR

[2] Agard S. B., Kelingos J., “On parametric representation for quasisymmetric functions”, Comm. Math. Helv., 44 (1969), 446–456 | DOI | MR | Zbl

[3] Alfors L., Lektsii po kvazikonformnym otobrazheniyam, Mir, M. | MR

[4] Anderson J. M., Becker J., Lesley F. D., “Boundary values of asymptotically conformal mapping”, J. London Math. Soc., 38:2 (1988), 453–462 | MR | Zbl

[5] Becker J., Pommerenke Ch., “Über die quasikonforme Fortsetzung schlichten Funktionen”, Math. Zeit., 161:1 (1978), 69–80 | DOI | MR | Zbl

[6] Belinskii P. P., Obschie svoistva kvazikonformnykh otobrazhenii, Nauka, Novosibirsk, 1974 | MR | Zbl

[7] Beurling A., Ahlfors L., “The boundary correspondence under quasiconformal mappings”, Acta Math., 96 (1956), 113–134 | DOI | MR

[8] Boyarskii B. V., “Obobschennye resheniya sistemy differentsialnykh uravnenii pervogo poryadka ellipticheskogo tipa s razryvnymi koeffitsientami”, Matem. sb., 43 (85) (1957), 451–503 | MR

[9] Carleson L., “On mappings conformal at the boundary”, J. Analyse Math., 19 (1967), 1–13 | DOI | MR | Zbl

[10] Douady A., Earle C. J., “Conformally natural extension of homeomorphisms of the circle”, Acta Math., 157 (1986), 23–48 | DOI | MR | Zbl

[11] Fehlmann R., “Über extremale quasikonforme Abbildungen”, Comment. Math. Helv., 56 (1981), 558–580 | DOI | MR | Zbl

[12] Gardiner F. P., Sullivan D. P., “Symmetric structures on a closed curve”, American J. of Math., 114 (1992), 683–736 | DOI | MR | Zbl

[13] Gehring F. W., “$L^p$-integrability of the partial derivatives of a quasiconformal mappings”, Acta Math., 130 (1973), 265–277 | DOI | MR | Zbl

[14] Gehring F. W., “Spirals and the universal Teichmüller space”, Acta Math., 141 (1978), 99–113 | DOI | MR | Zbl

[15] Gehring F. W., Lehto O., “On the total differetiability of functions of a complex variable”, Ann. Acad. Sci. Fenn. A I, 272 (1959) | MR | Zbl

[16] Gehring F. W., Reich E., “Area distortion under quasiconformal mappings”, Ann. Acad. Sci. Fenn. A I, 388 (1966), 1–15 | MR

[17] Gutlyanskii V. Ya., Ryazanov V. I., “O kvaziokruzhnostyakh i asimptoticheski konformnykh krivykh”, Dokl. RAN, 330:5 (1993), 546–548 | MR | Zbl

[18] Gutlyanskiǐ V. Ya., Ryazanov V. I., “On asymptotically conformal curves”, Complex Variables, 25 (1994), 1–10 | MR

[19] Hayman W. K., “The asymptotic behavior of $K$ q.s. functions”, Mathematical structures–Computational mathematics–Mathematical modelling, 2, Publishing House of BAS, Sofia, 1984, 198–207 | MR

[20] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1984 | MR | Zbl

[21] Kuratovskii K., Topologiya, T. 1, Mir, M., 1966 | MR

[22] Lehto O., Virtanen K., Quasikonforme Abbildungen, Springer-Verlag, Berlin etc., 1972 | MR

[23] Pommerenke Ch., Univalent functions, Vandenhoeck u. Ruprecht, Gottingen, 1975 | MR | Zbl

[24] Partyka D., “An alternative proof of a result due to Douady and Earle”, Annales Univ. Mariae Curie–Sklodowska, 42 (1988), 59–68 | MR | Zbl

[25] Reich E., Walczak H. R., “On the behavior of quasiconformal mappings at a point”, Trans. Amer. Math. Soc., 117:5 (1965), 338–351 | DOI | MR | Zbl

[26] Reimann H. M., “Ordinary differential equations and quasiconformal mappings”, Inventiones Math., 33 (1976), 247–270 | DOI | MR | Zbl

[27] Saks S., Teoriya integrala, IL, M., 1949

[28] Tukia P., “The space of quasisymmetric mappings”, Math. Scand., 40 (1977), 127–142 | MR | Zbl

[29] Schatz A., “On the local behavior of homeomorphic solutions of Beltrami's equation”, Duke Math. J., 35:2 (1968), 289–306 | DOI | MR | Zbl

[30] Teichmüller O., “Untersuchungen über konforme und quasikonforme Abbildung”, Deutsche Math., 3 (1938), 621–678 | Zbl

[31] Wittich H., “Zum Beweis eines Satzes über quasikonforme Abbildungen”, Math. Zeitschr., 51 (1948), 275–288 | DOI | MR