2008 DG-MP-PDE Seminar-17

We survey some recent results on Hessian, gradient estimates, regularity, and global rigidity for special Lagrangian equations with certain convexity. The gradient graph of the solutions are minimal Lagrangian submanifolds in Euclidean space. The special Lagrangian equations in the Pseudo-Euclidean setting are just Monge-Ampere equations, for which one has the corresponding classic results and counterexamples. This is partly joint work with Jingyi Chen and Micah Warren.