Boundary behavior of extremal plurisubharmonic functions
type: Item
instance of: scholarly article
title: Boundary behavior of extremal plurisubharmonic functions
zbMATH Open document ID: 0802.32024
DOI: 10.1007/BF02392790
author: Siegfried Momm
published in: Acta Mathematica
publication date: 1994-07-18T00:00:00Z
review text: Let \(G\) be a bounded convex domain in \(\mathbb{C}^ N\). The author introduces a function \(D_ G: \{z\in \mathbb{C}^ N: | z|=1\}\to ]0,\infty]\) (a kind of directional Lelong number) which measures the rate of approximation of \(\partial G\) by the level sets of the pluricomplex Green function for \(G\). The function \(D_ G\) is shown to be connected with the boundary behavior of the Siciak extremal plurisubharmonic function for \(G\). The problem of the boundedness of the function \(D_ G\) is considered.
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32W20
Mathematics Subject Classification ID: 31C10
zbMATH DE Number: 590324
zbMATH Keywords: convex domain
zbMATH Keywords: Green function
zbMATH Keywords: extremal plurisubharmonic function
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02392790
OpenAlex ID: W1992488517
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description: scientific article; zbMATH DE number 590324