Boundary behavior of the Bergman metric

Abstract

Let $\Omega$ be a bounded pseudoconvex domain in ${\bf C}^n$. We give sufficient conditions for the Bergman metric to go to infinity uniformly at some boundary point, which is stated by the existence of a Hölder continuous plurisubharmonic peak function at this point or the verification of property $(P)$ (in the sense of Coman) which is characterized by the pluricomplex Green function.