Gradient Bounds for Almost Complex Special Lagrangian Equation with Supercritical Phase

Abstract

In this article, we will consider the Dirichlet problem for special Lagrangian equation on $\Omega\subset M$, where $(M,J)$ is a compact almost complex manifold. Under the existence of $C^{2}$-smooth strictly $J$-plurisubharmonic subsolution $\underline{u}$, in the supercritical phase case, we  obtain a uniform global gradient estimate.