On the asymptotic expansion of complete Ricci-flat Kahler metrics on quasi-projective manifolds

Abstract

In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence of Kahler 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 the work of Tian-Yau, in particular obtaining their full asymptotic expansion.

This is the final version, December 2006