Geodesic
Extremal properties of mappings onto surfaces with parallel slits
Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 1-8

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In the present paper an are a theorem is established for certain regular functions associated with multivalent mappings of a finitely connected domain onto a surface with parallel slits. Several consequences of this theorem generalize well-known results from the theory of univalent conformal mappings. The notion of the generalized span of a domain is introduced. It is then shown that it possesses certain properties completely analogous to the basic extremal properties of the span of a domain. Grötzsch's theorem concerning the range of the first coefficient of the regular part of the normalized Laurent expansion of a univalent function about a pole is extended to multivalent functions. Bibliography: 7 titles. 
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Yu. E. Alenitsyn. Extremal properties of mappings onto surfaces with parallel slits. Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 1-8. http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a0/