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 
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/
@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},
     year = {1987},
     volume = {160},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a14/}
}
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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.