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

Abstract

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.