Singular scalar curvature equations

Abstract

We develop estimates for the equation of scalar curvature of singular metrics with cone angle $\beta >1$, in a big and semi-positive cohomology class on a Kähler manifold. We further derive the Laplacian estimate for the scalar curvature equation of degenerate Kähler metrics. We then have several applications of these estimates on the singular constant scalar curvature Kähler metrics, which also include the singular Kähler-Einstein metrics.