Geodesic
Sets of values of systems of functionals in classes of univalent functions
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 499-516

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The problem of describing the set of values of a system of functional $\{f(z),\dots,f^{(n)}(z)\}$ in the class of univalent functions holomorphic in the disk is formalized as a problem of constructing the set of attainability for a control system generated by the Löwner equation. In this problem the maximum principle turns out to be a necessary and sufficient condition for optimality. An algorithm for finding this set for a generalized Loewner equation with constant coefficients and continuous control is constructed. The results are extended to classes of bounded univalent functions. 
@article{SM_1992_71_2_a14,
     author = {D. V. Prokhorov},
     title = {Sets of values of systems of functionals in classes of univalent functions},
     journal = {Sbornik. Mathematics},
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     number = {2},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_2_a14/}
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D. V. Prokhorov. Sets of values of systems of functionals in classes of univalent functions. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 499-516. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a14/