Communications in Analysis and Geometry
Volume 14 (2006)
Higher canonical asymptotics of Kähler-Einstein metrics on quasi-projective manifolds
Pages: 795 – 845
We derive a canonical asymptotic expansion up to infinite order of the Kähler-Einstein metric on a quasi-projective manifold, which can be compactified by adding a divisor with simple normal crossings. Characterized by the log filtration of the Cheng-Yau Hölder ring, the asymptotics are obtained by constructing an initial Kähler metric, deriving certain iteration formula and applying the isomorphism theorems of the Monge-Ampère operators. This work is parallel to the asymptotics of Fefferman, Lee and Melrose on pseudoconvex domains in $C^n$.
2010 Mathematics Subject Classification
Primary 32Qxx. Secondary 53Cxx.