Geodesic
The module method and some extremal problems in the class $\Sigma(r)$
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 136-152 
G. V. Kuz'mina. The module method and some extremal problems in the class $\Sigma(r)$. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 136-152. http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a8/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\Sigma(r)$ denote some class of functions $f(z)$ meromorphic and univalent for $|z|>1$. In the class $\Sigma(r)$, some extremal problems are solved. The proofs are based on the module method.

[1] J. A. Jenkins, Univalent functions and conformal mapping, Ergeb. Math. Grenzgeb. (N.S.), 18, Springer-Verlag, 1958 ; 2nd ed., corrected, 1965; Dzh. Dzhenkins, Odnolistnye funktsii i konformnye otobrazheniya, M., 1962 | MR | Zbl

[2] J. A. Jenkins, “An extension of the general coefficient theorem”, Trans. Amer. Math. Soc., 95:3 (1960), 387–407 | DOI | MR | Zbl

[3] J. A. Jenkins, “On the existence of certain general extremal metrics. I”, Ann. Math. (2), 66 (1957), 440–453 ; “II”, Tohoku Math. J. (2), 45:2 (1993), 249–257 | DOI | MR | Zbl | DOI | MR | Zbl

[4] L. I. Kolbina, “Nekotorye ekstremalnye zadachi v konformnom otobrazhenii”, Dokl. AN SSSR, 84 (1952), 865–868 | MR | Zbl

[5] J. A. Jenkins, “A recent note of Kolbina”, Duke Math. J., 21 (1954), 155–161 | DOI | MR

[6] N. Suita, A distortion theorem of univalent functions related to symmetric three points, Kodai Math. Semin. Reports

[7] E. G. Emelyanov, G. V. Kuzmina, “Teoremy ob ekstremalnom razbienii v semeistvakh sistem oblastei razlichnykh tipov”, Zap. nauchn. semin. POMI, 237, 1997, 74–104 | MR | Zbl

[8] A. Yu. Solynin, “Moduli i ekstremalno-metricheskie problemy”, Algebra i analiz, 11:1 (1999), 3–86 | MR | Zbl

[9] G. V. Kuzmina, “Zadachi ob ekstremalnom razbienii i otsenki koeffitsientov v klasse $\Sigma(r)$”, Zap. nauchn. semin. POMI, 196, 1991, 101–116 | MR | Zbl