The minimum of the upper convex density of the product of the Cantor set with itself
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.
scientific article; zbMATH DE number 5324058