Whether p-conductive homogeneity holds depends on p

Shiping Cao, Zhen Qing Chen

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce two fractals, in Euclidean spaces of dimension two and three, respectively, such that the 2-conductive homogeneity holds but there is some " 2 .0; 1/ so that the p-conductive homogeneity fails for every p 2 .1; 1 C "/. In addition, these two fractals have Ahlfors regular conformal dimension within the interval .1; 2/ and .2; 3/, respectively.

Original languageEnglish
Pages (from-to)93-104
Number of pages12
JournalJournal of Fractal Geometry
Volume12
Issue number1-2
DOIs
Publication statusPublished - 2025
Externally publishedYes

Keywords

  • conductance
  • Dirichlet form
  • energy measure
  • extension operator
  • harmonic function
  • Mosco convergence
  • Sierpiński carpets
  • weak convergence

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