Estimates of Invariant Metrics on Pseudoconvex Domains Near Boundaries with Constant Levi Ranks

摘要

Estimates of the Bergman kernel and the Bergman and Kobayashi metrics on pseudoconvex domains near boundaries with constant Levi ranks are given. As a consequence, a characterization of Levi-flatness in terms of boundary behavior of the Bergman and Kobayashi metrics is obtained.