  We consider the Gaussian curvature conjecture of a minimal graph $S$ over the
unit disk. First of all we reduce the general conjecture to the estimating the
Gaussian curvature of some Scherk's type minimal surfaces over a quadrilateral
inscribed in the unit disk containing the origin inside. As an application we
improve so far the obtained upper estimates of Gaussian curvature at the point
above the center. Further we obtain an optimal estimate of the Gaussian
curvature at the point $\mathbf{w}$ over the center of the disk, provided
$\mathbf{w}$ satisfies certain "symmetric" conditions. The result extends a
classical result of Finn and Osserman in 1964. In order to do so, we construct
a certain family $S^t$, $t\in[t_\circ, \pi/2]$ of Scherk's type minimal graphs
over the isosceles trapezoid inscribed in the unit disk. Then we compare the
Gaussian curvature of the graph $S$ with that of $S^t$ at the point
$\mathbf{w}$ over the center of the disk.
