Behavior of the Bergman kernel at infinity
type: Item
instance of: scholarly article
title: Behavior of the Bergman kernel at infinity
zbMATH Open document ID: 1066.32003
author: Boyong Chen
author: Joe Kamimoto
author: Takeo Ohsawa
published in: Mathematische Zeitschrift
publication date: 2005-02-02T00:00:00Z
review text: The authors study the behavior at infinity of the Bergman kernel function and the Bergman metric on unbounded model domains in \(\mathbb{C}^{n+1}\) of the form \(\{\,(z,w): \Im w > \rho(z)\,\}\), where \(\rho\)~is a non-negative plurisubharmonic function on~\(\mathbb{C}^n\) that tends to infinity with~\(\| z\| \). They show first of all that the Bergman kernel function is non-trivial and the Bergman metric is complete. Moreover, in any tubular neighborhood of the complex line \(z=0\) in~\(\mathbb{C}^{n+1}\), the Bergman kernel on the diagonal at \((z,w)\) tends to zero faster than \((\Im w)^{-2}\) as \(\Im w \to \infty\). Additionally, the authors obtain precise estimates on the size at infinity of the Bergman kernel and Bergman metric under various special hypotheses on the growth of~\(\rho\).
reviewed by: Harold P. Boas
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32F45
zbMATH DE Number: 2132000
zbMATH Keywords: Bergman metric
zbMATH Keywords: unbounded domain
zbMATH Keywords: Haslinger's formula
MaRDI profile type: Publication
full work available at URL: s00209-004-0676-6
OpenAlex ID: W2034947139
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DOI: 10.1007/S00209-004-0676-6
description: scientific article; zbMATH DE number 2132000