An application from partial sums of \(e^ z\) to a problem in several complex variables (Q1802174)

\textit{I. Graham} has conjectured in Complex Variables, Theory Appl. 15, No. 1, 37-42 (1990; Zbl 0681.32002) the following \(n\)-dimensional version of the Koebe 1/4 theorem: Given an \(m\)-degree polynomial mapping \(f\) of \(\mathbb{C}^ n\) into \(\mathbb{C}^ n\), there exists a positive constant \(a_ m\) such that \(Hf(B_ 1)\supset B_{a_ m}\), where \(B_ r\) is the ball with radius \(r\) and \(HX\) is the closed convex hull of \(X\). In this paper it is proved that this conjecture holds.