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Behavior of the Bergman kernel and metric near convex boundary points


Authors: Nikolai Nikolov and Peter Pflug
Journal: Proc. Amer. Math. Soc. 131 (2003), 2097-2102
MSC (2000): Primary 32A25
DOI: https://doi.org/10.1090/S0002-9939-03-07030-8
Published electronically: February 11, 2003
MathSciNet review: 1963755
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Abstract: The boundary behavior of the Bergman metric near a convex boundary point $z_0$ of a pseudoconvex domain $D\subset\mathbb{C}^n$ 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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Additional Information

Nikolai Nikolov
Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Email: nik@math.bas.bg

Peter Pflug
Affiliation: Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany
Email: pflug@mathematik.uni-oldenburg.de

DOI: https://doi.org/10.1090/S0002-9939-03-07030-8
Keywords: Bergman kernel, Bergman metric
Received by editor(s): January 21, 2002
Published electronically: February 11, 2003
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2003 American Mathematical Society