Asymptotic behavior of the curvature of the Bergman metric of the thin domains
type: Item
instance of: scholarly article
title: Asymptotic behavior of the curvature of the Bergman metric of the thin domains
zbMATH Open document ID: 0723.32009
author: Kang-Tae Kim
published in: Pacific Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: This paper presents a method that studies the boundary behavior of the Riemann sectional curvature tensor of the Bergman metric of pseudoconvex domains which are a `small and thin' intersection of finitely many strongly pseudoconvex domains. The main result, roughly speaking, is that the limit of the Riemann sectional curvature tensor of the Bergman metric of such domains is that of a Siegel domain evaluated at a specific point, where the Siegel domain and the point are determined explicitly by the (piecewise smooth) local defining function of the domain near the boundary point in consideration and by the manner the point sequences approaches the boundary point in question from the interior of the original domain. The paper treats only the case of such `thin\(>\) domains. But the method in it is also applicable to a broader class containing certain weakly pseudoconvex domains.
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 4192113
zbMATH Keywords: piecewise smooth boundary
zbMATH Keywords: boundary behavior
zbMATH Keywords: Riemann sectional curvature tensor
zbMATH Keywords: Bergman metric
zbMATH Keywords: pseudoconvex domains
MaRDI profile type: Publication
full work available at URL: pjm.1992.155.99
OpenAlex ID: W1972955942
DOI: 10.2140/PJM.1992.155.99
description: scientific article; zbMATH DE number 4192113