The regularity theory of the degenerate complex Monge-Amp\`{ e}re equation is studied. The equation is considered on a closed compact K\"{ a}hler manifold $(M,g)$ with nonnegative orthogonal bisectional curvature of dimension $m$. Given a solution $\phi$ of the degenerate complex Monge-Amp\`{ e}re equation $\det(g_{ i \bar{ j}} + \phi_{ i \bar{ j}}) = f \det(g_{ i \bar{ j}})$, it is shown that the Laplacian of $\phi$ can be controlled by a constant depending on $(M,g)$, $\sup f$, and $\inf_M \Delta f^{ 1/(m-1)}$.
Categories: math.AP math.CV