Geodesic
About distortion theorems for one class quasi-conformal mappings, conformal outside a ring
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2009), pp. 65-74 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author considers the class of quasiconformal homeomorphisms of extended complex plane onto itself, such as $f(\infty)=\infty$, $f'(\infty)=1$, $f(0)=0$. The area theorem was derived in the form of inequality for Grunsky coefficients. This inequality can be used for estimate functionals such as distortion theorems. Sufficient conditions of univalence functions $f(z)$ of this class are given.
Keywords: quasi-conformal homeomorphism, Grunsky coefficients, area theorems.
Mots-clés : conditions of univalence 
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V. A. Shchepetev. About distortion theorems for one class quasi-conformal mappings, conformal outside a ring. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2009), pp. 65-74. http://geodesic.mathdoc.fr/item/VTGU_2009_4_a5/

[1] Pommerenke Chr., Univalent Functions, Vandenhoeck Ruprecht, Gottingen, 1975 | MR | Zbl

[2] Grunsky H., “Koeffizientenbedingungen for schlicht abbildende meromorpfe Functionen”, Math. Z., 45:1, 29–61 | DOI | MR | Zbl

[3] Lebedev N.A., Printsip ploschadei v teorii odnolistnykh funktsii, Nauka, M., 1975, 336 pp. | Zbl

[4] Schepetev V.A., “Teorema ploschadei dlya odnogo klassa kvazikonformnykh otobrazhenii”, DAN Ukrainskoi SSR. Seriya A, 1979, no. 8, 618–621

[5] Gutlyanskii V.Ya., “O printsipe ploschadei dlya odnogo klassa kvazikonformnykh otobrazhenii”, DAN SSSR, 212:3 (1973), 540–543 | MR | Zbl

[6] Kühnau R., “Verzerrungssätze und Koeffizientenbedingungen vom Grunskyschen Typ für quasikonforme Abbildungen”, Math. Nachr., 48:1-6 (1971), 77–105 | DOI | MR | Zbl

[7] Lehto O., “Schlicht functions with a quasiconformal extension”, Ann. Acad. Sci. Fenn., Ser. AI, 1971, no. 500, 10 pp. | MR | Zbl