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 an(f) zn

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 a2(f) and a3(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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