Geodesic
Area theorems for functions analytic in a~finitely connected domain
Izvestiya. Mathematics , Tome 7 (1973) no. 5, pp. 1129-1151

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In this paper we consider functions analytic in a given finitely connected domain apart from a finite number of singularities of possibly logarithmic type. We prove some area theorems which generalize to these functions certain known results, in particular Goluzin's area theorem on functions $p$-valent in a disc. We establish some integral criteria of when functions meromorphic in a given multiply-connected domain are univalent functions there and pairwise without common values. 
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     author = {Yu. E. Alenitsyn},
     title = {Area theorems for functions analytic in a~finitely connected domain},
     journal = {Izvestiya. Mathematics },
     pages = {1129--1151},
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Yu. E. Alenitsyn. Area theorems for functions analytic in a~finitely connected domain. Izvestiya. Mathematics , Tome 7 (1973) no. 5, pp. 1129-1151. http://geodesic.mathdoc.fr/item/IM2_1973_7_5_a7/