Higher canonical asymptotics of Kahler-Einstein metrics on quasi-projective manifolds

摘要

We derive a canonical asymptotic expansion up to infinite order of the Kahler-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 Holder ring, the asymptotics are obtained by constructing an initial Kahler metric, deriving certain iteration formula and applying the isomorphism. theorems of the Monge-Ampere operators. This work is parallel to the asymptotics of Fefferman, Lee and Melrose on pseudoconvex domains in C-n.