Values of Gauss maps of complete minimal surfaces in ${\mathbb{R}}^{m}$ on annular ends

Let $M$ be a complete minimal surface in ${\mathbb{R}}^{m}$ and let $A$ be an annular end of $M$ which is conformal to $\{z~\vert~ 0 < 1/r<\vert z\vert<r\}$, where $z$ is the conformal coordinate. Let $G$ be the generalized Gauss map of $M$. We show that $G(A)$ must intersect every hyperplane in ${\mathbb{P}}^{m-1}({\mathbb{C}})$, with the possible exception of $m(m+1)/2$ hyperplanes in general position.