Communications in Analysis and Geometry
Volume 16 (2008)
Kähler-Einstein metrics of negative Ricci curvature on general quasi-projective manifolds
Pages: 395 – 435
In this paper, we give sufficient and necessary conditions for the existence of a Kähler-Einstein metric on a quasi-projective manifold of finite volume, bounded Riemannian sectional curvature and Poincaré growth near the boundary divisor. These conditions are obtained by solving a degenerate Monge-Ampère equation andderiving the asymptotics of the solution.