The analyticity of \(q\)-concave sets of locally finite \((2n-2q)\)-dimensional Hausdorff measure
type: Item
instance of: scholarly article
title: The analyticity of \(q\)-concave sets of locally finite \((2n-2q)\)-dimensional Hausdorff measure
zbMATH Open document ID: 0974.32006
publication date: 2000-07-19T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75453
review text: In the context of finding reasonable assumptions on a closed subset \(A\) of an analytic space \(X\) in order to guarantee that \(A\) is itself analytic, the paper is devoted to the proof of the following result: If \(X\) is a complex space of pure dimension \(n\), \(q\) is a positive integer less than \(n\) and \(A\) is a \(q\)-concave subset in \(X\) whose Hausdorff \((2n-2q)\)-measure is locally finite, then \(A\) is analytic of pure dimension \(n-q\). A relation with the notion of \(q\)- pseudoconcavity considered by \textit{M. Peternell} in [Invent. Math. 85, 249-262 (1986; Zbl 0599.32016)] is also presented.
reviewed by: Eugen Pascu
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32C25
zbMATH DE Number: 1478819
zbMATH Keywords: \(q\)-convexity
zbMATH Keywords: \(q\)-concavity
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: analytic set
author: Viorel Vâjâitu
MaRDI profile type: Publication
OpenAlex ID: W2493077197
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DOI: 10.5802/AIF.1789
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1478819