A PRIORI ESTIMATES OF THE DEGENERATE MONGE-AMPERE EQUATION ON KAHLER MANIFOLDS OF NON-NEGATIVE BISECTIONAL CURVATURE

The regularity theory of the degenerate complex Monge-Ampere equation is studied. The equation is considered on a closed compact Kahler manifold (M, g) with non-negative orthogonal bisectional curvature of dimension m. Given a solution phi of the degenerate complex Monge-Ampere equation det(gi (j) over bar vertical bar phi i (j) over bar) = f det(gi (j) over bar), 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)).