Geodesic
A class of functions that are univalent in an annulus
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 83-93 
E. G. Emel'yanov. A class of functions that are univalent in an annulus. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 83-93. http://geodesic.mathdoc.fr/item/ZNSL_1985_144_a8/
@article{ZNSL_1985_144_a8,
     author = {E. G. Emel'yanov},
     title = {A class of functions that are univalent in an annulus},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {83--93},
     year = {1985},
     volume = {144},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_144_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the class $F_1$ of functions $f(\zeta)$, regular and univalent in the annulus $K=\{\rho<|\zeta|<1\}$ and satisfying the conditions $|f(\zeta)|<1$ and $f(\zeta)\ne0$ for $\zeta\in K$, $|f(\zeta)|=1$, $|\zeta|=1$, for $f(1)=1$, one finds the set of the values $D(A)=\{f(A):f\in K\}$ for an arbitrary fixed point $A\in K$. One makes use of the method of variations and certain facts from the theory of the moduli of families of curves.