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

TL;DR

This paper analyzes the detailed asymptotic behavior of complete Ricci-flat Kähler metrics on quasi-projective manifolds, providing explicit constructions and full asymptotic expansions of solutions.

Contribution

It introduces explicit approximating metrics and derives the complete asymptotic expansion of Tian-Yau solutions on open Kähler manifolds.

Findings

Explicit sequence of Kähler metrics constructed

Full asymptotic expansion of Ricci-flat metrics obtained

Enhanced understanding of metric behavior near divisors

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.