Behavior of the Bergman kernel and metric near convex boundary points

Details Behavior of the Bergman kernel and metric near convex boundary points Behavior of the Bergman kernel and metric near convex boundary points

2002-01-10

arxiv.org/abs/math/0201088v1

Mathematics

Complex Variables

Scientific paper

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

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