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 Ω ⊂ M, where (M, J) is a compact almost complex manifold. Under the existence of C 2 -smooth strictly J-plurisubharmonic subsolution u, in the supercritical phase case, we obtain a uniform global gradient estimate.