RIGIDITY FOR GENERAL SEMICONVEX ENTIRE SOLUTIONS TO THE SIGMA-2 EQUATION

We show that every general semiconvex entire solution to the sigma-2 equation is a quadratic polynomial. A decade ago, this result was shown for almost convex solutions. Two decades ago, this result was obtained in three dimensions, as a byproduct of the work on special Lagrangian equations. Warren's rare saddle entire solution in 2014 confirmed the necessity of the semiconvexity assumption.