Communications in Analysis and Geometry

Volume 16 (2008)

Number 2

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

Pages: 395 – 435

DOI: http://dx.doi.org/10.4310/CAG.2008.v16.n2.a4

Author

Damin Wu

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.

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