Estimates of Kähler-Einstein metrics on pseudoconvex domains of finite type with locally diagonalizable Levi form

Abstract

In this short note, we use the weights introduced by Ph. Charpentier and Y. Dupain on pseudoconvex domains of finite type with locally diagonalizable Levi form to prove that on these domains, the Kähler-Einstein metrics are comparable with the Carathéodory, Kobayashi and Bergman metrics.