Geodesic
On some questions connected with the problem of existence of automorphic analytic functions with given modulus of boundary values
Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 501-518

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For an arbitrary region $D$ in the extended plane it is shown that the possibility of constructing automorphic analytic functions with given modulus of boundary values on the universal covering surface of $D$ is a local property of the boundary of $D$ and is equivalent to the possibility of giving a good description of the extremals for a rather large class of problems in this region. Bibliography: 12 titles. 
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     author = {M. V. Samokhin},
     title = {On some questions connected with the problem of existence of automorphic analytic functions with given modulus of boundary values},
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M. V. Samokhin. On some questions connected with the problem of existence of automorphic analytic functions with given modulus of boundary values. Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 501-518. http://geodesic.mathdoc.fr/item/SM_1981_39_4_a4/