Kahler-Einstein metrics of negative Ricci curvature on general quasi-projective manifolds

摘要

In this paper, we give sufficient and necessary conditions for the existence of a Kahler-Einstein metric on a quasi-projective manifold of finite volume, bounded Riemannian sectional curvature and Poincare growth near the boundary divisor. These conditions are obtained by solving a degenerate Monge-Ampere equation and deriving the asymptotics of the solution.