Geodesic
Differential inequalities in linear- and affine-invariant families of harmonic mappings
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2010), pp. 69-72.

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At the linear- and affine-invariant families of harmonic mappings of the unit disk some differential inequalities such as sharp estimation of the Jacobian and estimation of curvature of the image of the circle are proved.
Keywords: harmonic mappings, linear- and affine-invariant families functions, order of family. 
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S. Yu. Graf; O. R. Eyelangoli. Differential inequalities in linear- and affine-invariant families of harmonic mappings. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2010), pp. 69-72. http://geodesic.mathdoc.fr/item/IVM_2010_10_a6/

[1] Pommerenke Ch., “Linear-invariante Familien analytischer Funktionen. I”, Math. Ann., 155 (1964), 108–154 | DOI | MR | Zbl

[2] Sheil-Small T., “Constants for planar harmonic mappings”, J. Lond. Math. Soc. II Ser., 42:2 (1990), 237–248 | DOI | MR | Zbl

[3] Starkov V. V., “Harmonic locally quasiconformal mappings”, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 49:14 (1995), 183–197 | MR | Zbl

[4] Graf S. Yu., “Tochnaya otsenka yakobiana v lineino- i affinno-invariantnykh semeistvakh garmonicheskikh otobrazhenii”, Tr. Petrozavodsk. gos. un-ta. Ser. Matem., 14, 2007, 31–38 | MR | Zbl

[5] Clunie J., Sheil-Small T., “Harmonic univalent functions”, Ann. Acad. Sci. Fenn. Ser. A I, 9 (1984), 3–25 | MR | Zbl

[6] Graf S. Yu., “Teoremy iskazheniya v semeistvakh garmonicheskikh otobrazhenii”, Trans. Acad. Sci. Ukraine (to appear)

[7] Duren P., Harmonic mappings in the plane, Cambridge University Press, Cambridge, 2004 | MR | Zbl