Zero-curvature point of minimal graphs

Motivated by a classical result of Finn and Osserman (J Anal Math 343(12):351–364, 1964), who proved that the Jenkins–Serrin graph over square inscribed in unit disk is extremal for Gaussian curvature point O (so-called centre) minimal graphs above center 0 disk, provided tangent plane horizontal, we ask answer to question concerned "second derivative" such its at zero. We prove extremals are certain regular hexagon vanishes horizontal centre.