A class of functions that are univalent in an annulus

E. G. Emel'yanov

Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 83-93

Résumé

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.