Geodesic
Some extremal problems for pairs of functions without common values
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 159-169

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By the method of the moduli of families of curves one solves some extremal problems in the family of pairs $\{f_1,f_2\}$ of functions $f_1(z)=\alpha z+\dotsb$, $f_2(z)=\beta z^{-1}+\beta_0+\beta_1z+\dotsb$, with real coefficients, univalent, regular, resp. meromorphic in the circle $\Delta=\{|z|1\}$ and mapping onto nonoverlapping domains. As a special case the solution of a problem, posed by V.M. Miklyukov in Sib. Mat. Zh., Vol. 18, 1977, No. 5, pp. 1111–1124, is obtained. 
@article{ZNSL_1987_160_a14,
     author = {A. Yu. Solynin},
     title = {Some extremal problems for pairs of functions without common values},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {159--169},
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     volume = {160},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a14/}
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A. Yu. Solynin. Some extremal problems for pairs of functions without common values. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 159-169. http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a14/