Doubling Argument of the Hessian Estimate for the Special Lagrangian Equation on General Phases with Constraints

Abstract

In this paper, we establish a doubling argument to obtain Hessian estimates for the special Lagrangian equation under general phase constraints. In particular, our approach does not rely on the Michael-Simon mean value inequality. As an intermediate step, we also establish Alexandrov-type theorems, which may be of independent interest.