Geodesic
The Existence of Quadratic Differentials in Simply Connected Regions of the Complex Plane
Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 83-91

Voir la notice de l'article provenant de la source Cambridge University Press

The general coefficient theorem [2] and the extended general coefficient theorem [3] state that the existence of certain quadratic differentials is a sufficient condition for a function to be a solution of certain extremum problems. The purpose of this paper is to show that in the case of simply connected regions this condition is also necessary.We shall do this by a variational method of the Schiffer-Golusin-type. The main difficulty is, that the class of admissible functions for the general coefficient theorem is restricted and we must therefore have a method of variation with restrictions. 
Grassmann, E. The Existence of Quadratic Differentials in Simply Connected Regions of the Complex Plane. Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 83-91. doi: 10.4153/CJM-1973-006-4
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[1] 1. Golusin, G. M., GeometrischeFunktionentheorie(DeutscherVerlag der Wissenschaften, Berlin, 1957). Google Scholar

[2] 2. Jenkins, T. A., Univalent functions, 2nd Ed. (Springer, Berlin, 1965). Google Scholar

[3] 3. Jenkins, T. A., On certain extremal problems for the coefficients of univalent functions, J. Analyse Math. 18 (1967) Google Scholar

[4] 4. Lang, S., Analysis. I (Addison Wesley, Reading, 1968). Google Scholar

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