Behavior of the Bergman kernel and metric near convex boundary points

Nikolov, Nikolai; Pflug, Peter

doi:10.1090/S0002-9939-03-07030-8

Behavior of the Bergman kernel and metric near convex boundary points
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Proc. Amer. Math. Soc. 131 (2003), 2097-2102 Request permission

Abstract:

The boundary behavior of the Bergman metric near a convex boundary point $z_0$ of a pseudoconvex domain $D\subset \mathbb {C}^n$ is studied. It turns out that the Bergman metric at points $z\in D$ in the direction of a fixed vector $X_0\in \mathbb {C}^n$ tends to infinity, when $z$ is approaching $z_0$, if and only if the boundary of $D$ does not contain any analytic disc through $z_0$ in the direction of $X_0$.

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