Pluripolarity of sets with small Hausdorff measure
type: Item
instance of: scholarly article
title: Pluripolarity of sets with small Hausdorff measure
zbMATH Open document ID: 0964.32030
author: D. A. Labutin
published in: Manuscripta Mathematica
publication date: 2001-07-08T00:00:00Z
review text: Let \(H(r)= (\log\frac 1r)^{-n}\), \(n\geq 2\). The author proves that any set \(E\subset\mathbb{C}^n\), \(n\geq 2\), with finite Hausdorff measure \(\Lambda_{H}(E)\leq\infty\) is pluripolar. The result is sharp with respect to the measuring function, i.e., for any measuring function \(h\) such that \[ \liminf_{r\to 0}\frac{h(r)}{H(r)}=0 \] there exists a set \(E\subset\mathbb{C}^n\) such that \(\Lambda_{h}(E)=0\) but \(E\) is not pluripolar.
Mathematics Subject Classification ID: 32U15
Mathematics Subject Classification ID: 32U20
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 31C10
zbMATH DE Number: 1491673
zbMATH Keywords: pluripolar (polar) set
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: Bedford-Taylor capacity
zbMATH Keywords: measuring function
zbMATH Keywords: plurisubharmonic function
MaRDI profile type: Publication
full work available at URL: s002291020163
OpenAlex ID: W1979124028
DOI: 10.1007/S002291020163
description: scientific article; zbMATH DE number 1491673