Special Lagrangian equations

In joint work with Yu Yuan, we prove a priori interior estimates for special Lagrangian equations. In particular, we show interior a priori Hessian estimates for solutions of the sigma2-equation in dimension three s2D2u =l1l2+l2 l3+l3l1 =1.;We show Hessian estimates for large phase special Lagrangian equations in dimension three, and give sharper estimates for dimension two. We also show gradient estimates for large phase special Lagrangian equations. In joint work with Jingyi Chen and Yu Yuan, we show Hessian estimates for convex solutions in arbitrary dimension. In chapter two, we discuss Monge-Ampere equations in the context of calibrated Lagrangian geometry.