Boundary behaviour of the Bergman invariant and related quantities
type: Item
instance of: scholarly article
title: Boundary behaviour of the Bergman invariant and related quantities
zbMATH Open document ID: 1147.32005
published in: Monatshefte für Mathematik
publication date: 2008-05-27T00:00:00Z
full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary
review text: The boundary behaviour of the Bergman kernel has been known since the 1974 seminal work of Fefferman. Using Fefferman's classical result on the boundary singularity of the Bergman kernel, this paper gives an analogous complete description of the boundary singularity of various related quantities like the Bergman invariant, the coefficients of the Bergman metric, of the associated Laplace-Beltrami operator, of its curvature tensor, Ricci curvature and scalar curvature. The main point is that even though one would expect a bit stronger singularities than the one for the Bergman kernel, due to the differentiations involved, all these quantities turn out to have -- except for a different leading power of the defining function -- the same kind of singularity as the solution of the Monge-Ampère equation.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32A36
zbMATH DE Number: 5279074
zbMATH Keywords: Bergman kernel
zbMATH Keywords: Bergman invariant
zbMATH Keywords: Bergman metric
zbMATH Keywords: singularity
author: Miroslav Engliš
reviewed by: Ze-Hua Zhou
MaRDI profile type: Publication
OpenAlex ID: W2061304330
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DOI: 10.1007/S00605-008-0522-8
description: scientific article; zbMATH DE number 5279074