An integral inequality of an intrinsic measure on bounded domains in \({\mathbb{C}{}}^ n\)
type: Item
instance of: scholarly article
title: An integral inequality of an intrinsic measure on bounded domains in \({\mathbb{C}{}}^ n\)
zbMATH Open document ID: 0776.32014
author: S. Singh
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-05-16T00:00:00Z
review text: Let \(K_ D\) denote the Eisenman-Kobayashi volume element (defined using the unit ball) on a strongly pseudoconvex domain \(D\) in \(\mathbb{C}^ n\). \textit{I. Graham} and \textit{H. Wu} [Trans. Am. Math. Soc. 288, No. 2, 625- 660 (1985; Zbl 0582.32034)] have shown that \(K_ D\) need not be logarithmically plurisubharmonic. The authors prove that \(K_ D\) satisfies an integral inequality, weaker than logarithmic plurisubharmonicity, on analytically embedded disks sufficiently close to the boundary of \(D\). Moreover, a similar inequality holds for any bounded domain on which the Eisenman-Kobayashi volume element satisfies a suitable boundary growth condition.
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32F45
zbMATH DE Number: 168030
zbMATH Keywords: Eisenman-Kobayashi volume element
zbMATH Keywords: integral inequality
reviewed by: Theodore J. Barth
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072698
OpenAlex ID: W2082675054
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DOI: 10.1216/RMJM/1181072698
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description: scientific article; zbMATH DE number 168030