## Abstract

In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kähler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct an explicit sequence of Kähler metrics with special approximating properties. Using those metrics as starting point, we are able to work out the asymptotic behavior of the solutions given in *Tian, Gang, Yau, Shing-Tung*, Complete Kähler manifolds with zero Ricci curvature. I, J. Amer. Math. Soc. 3 (1990), no. 3, 579–609., in particular obtaining their full asymptotic expansion.

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