## F.G. Avkhadiev K.-J. Wirths

# Concave schlicht functions with bounded opening angle at infinity

## (Lobachevskii Journal of Mathematics, Vol.17, pp.3 - 10)

Let D denote the open unit disc.
In this article we consider functions

f(z)=z + ∑_{n=2}^{∞} a_{n}(f) z^{n}

that map D conformally onto a domain whose complement with respect to
C is convex and that satisfy the normalization
f(1)=∞. Furthermore, we impose on these functions the condition
that the opening angle of f(D) at infinity is less than or equal to
π A, A ∈ (1,2]. We will denote these families of functions by
CO(A). We get
representation formulas for the functions in CO(A). They enable us
to derive the exact domains of variability of a_{2}(f) and a_{3}(f),
f ∈ CO(A). It turns out that the boundaries of these domains in both
cases are described by the coefficients of the conformal maps of D
onto angular domains with opening angle π A.

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