The minimum of the upper convex density of the product of the Cantor set with itself
type: Item
instance of: scholarly article
title: The minimum of the upper convex density of the product of the Cantor set with itself
zbMATH Open document ID: 1160.28001
author: Li Feng
author: Zuoling Zhou
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-09-10T00:00:00Z
review text: The authors consider a property of upper convex density of the product of the Cantor set. Let \(C \times C\) be the product of the middle third Cantor set with itself, the authors prove that the minimum of the upper convex density of \(C\times C\) is achieved at the vertex, that is, \({\bar D}^s_C ({C\times C},V)\leq {\bar D}^s_C({C \times C},x)\), \(\forall x\in {C\times C}\), where \(V\) is a vertex of \(C\times C\). It will be an interesting problem to determine exactly this minimum.
reviewed by: Hua Su
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 5324058
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: upper convex density
zbMATH Keywords: self-similar set
MaRDI profile type: Publication
full work available at URL: j.na.2007.03.035
OpenAlex ID: W2058853794
cites work: Q3714302
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DOI: 10.1016/J.NA.2007.03.035
description: scientific article; zbMATH DE number 5324058