Behavior of the Bergman kernel and metric near convex boundary points

Nikolai Nikolov; Peter Pflug

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arXiv · math/0201088

Behavior of the Bergman kernel and metric near convex boundary points

Nikolai Nikolov·Peter Pflug

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Abstract

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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Nikolai Nikolov, Peter Pflug. 2002-01-10. Behavior of the Bergman kernel and metric near convex boundary points. https://arxiv.org/abs/math/0201088

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