A Liouville-type theorem for the equation of special Lagrangian manifolds (Q1324898)

The author considers solutions of the equation \[ \text{det}\left({\partial^ 2 f\over \partial x_ i \partial x_ j}\right) = \sum^ n_{i,j = 1} {\partial^ 2 f\over \partial x_ i \partial x_ j} \tag{*} \] for any \(n\), defined over the whole plane of variables \(x_ 1,x_ 2,\dots, x_ n\). The author proves the following result: a convex solution of class \(C^ 2\) of equation (*) that increases at most linearly at infinity is linear.