Power series with Hadamard gaps and hyperbolic complete minimal surfaces (Q1210425)

F. Xavier -- L. P. M. Jorge and R. Kunert proved independently and simultaneously the existence of complete minimal surfaces between two parallel planes in \(\mathbb{R}^ 3\). Xavier and Jorge use Runge's approximation theorem, R. Kunert needs the universal covering of Riemann surfaces. Both proofs give no clue on how to construct examples. In the present paper a new method is developed to construct explicitly a large family of minimal surfaces with the properties mentioned above. The author uses some special power series with Hadamard gaps to get the \(g\)- function in the Weierstraß representation formula.