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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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On the asymptotic expansion of complete Ricciflat Kähler metrics on quasi-projective manifolds

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2008, Issue 615, Pages 59–91, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2008.010, March 2008

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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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