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

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.

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Published 1 January 2008