We derive a Bernstein type result for the special Lagrangian equation, namely, any global convex solution must be quadratic. In terms of minimal surfaces, the result says that any global minimal Lagrangian graph with convex potential must be a hyper-plane.Comment: 9 pages, submitted on December 10, 200

We show that (a) any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C m with the Euclidean metric is flat; (b) any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C m with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the Kähler Ricci flow.

We derive a priori interior Hessian estimates for the special Lagrangian equation 2 D 1 in dimension 3.

We show that any global solution to the special Lagrangian equations with the phase larger than a critical value must be quadratic.