Classification of doubly-periodic minimal surfaces of genus zero (Q1592910)

The authors give a proof of the result announced by them in [C. R. Acad. Sci., Paris, Sér. I, Math. 325, 753-754 (1997; Zbl 0884.53046)]. If the quotient surface of a properly embedded doubly-periodic minimal surface in \(\mathbb{R}^3\) has genus zero, then it is one of the classical Scherk examples. The proof is substantially different from the one presented in the first author's PhD thesis [Surfaces minimales doublement périodiques, Ecole Polytechnique (1997)].