On degenerate Monge-Ampere equations over closed Kahler manifolds

Abstract

In this short paper, we study complex Monge-Ampère equations over closed Kähler manifolds. The generalization from classic case is that the cohomology class can be no longer Kähler. The center of the argument is to derive a priori L∞ estimate for the solution. With some help from a classic result in several complex variables, we can prove the continuity of the solution for the most interesting case. Our proof makes use of pluripotential theory and is a quite direct generalization of the works of S. Kolodziej.