CR invariants of weight five in the Bergman kernel
type: Item
instance of: scholarly article
title: CR invariants of weight five in the Bergman kernel
zbMATH Open document ID: 0932.32005
author: Kengo Hirachi
author: Gen Komatsu
published in: Advances in Mathematics
publication date: 2000-03-06T00:00:00Z
review text: This article continues the development of Fefferman's program [\textit{Ch. Fefferman}, Adv. Math. 31, 131-262 (1979; Zbl 0444.32013)] to express the asymptotic expansion of the Bergman kernel function on the diagonal near the boundary of a strongly pseudoconvex domain in \(\mathbf{C}^n\) in terms of CR invariants of the boundary. The authors also study the Szegő kernel function. The paper refines earlier results of \textit{C. R. Graham} [Lect. Notes Math. 1276, 108-135 (1987; Zbl 0626.32027)] and the authors [Komatsu, Gen (ed.) et al., Lect. Notes Pure Appl. Math. 143, 77-96 (1993; Zbl 0793.32009)] by identifying the coefficients in the expansion through the invariants of weight \(\leq 5\) when the dimension \(n=2\). For further advances on the singularity of the Bergman kernel function in \(\mathbf{C}^n\), see a paper of the first author [Construction of boundary invariants and the logarithmic singularity in the Bergman kernel, Ann. Math., to appear].
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 1295248
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: Weyl invariant
zbMATH Keywords: Szegő kernel function
zbMATH Keywords: strongly pseudoconvex domain
zbMATH Keywords: complex Monge-Ampère equation
reviewed by: Harold P. Boas
MaRDI profile type: Publication
OpenAlex ID: W2015127645
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DOI: 10.1006/AIMA.1998.1794
description: scientific article; zbMATH DE number 1295248