In this paper, we study the singular Monge–Ampère equations on a quasi–projective manifold with a Poincaré metric. As a consequence, we construct Poincaré Kähler–Einstein metrics which degenerate or grow upward at most like a pole along a given effective divisor.
"Good Kähler Metrics with Prescribed Singularities." Asian J. Math. 13 (1) 131 - 150, March 2009.