Whether p-conductive homogeneity holds depends on p

Shiping Cao; Zhen Qing Chen

doi:10.4171/JFG/156

Whether p-conductive homogeneity holds depends on p

Shiping Cao
, Zhen Qing Chen

University of Washington

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	93-104
Number of pages	12
Journal	Journal of Fractal Geometry
Volume	12
Issue number	1-2
DOIs	https://doi.org/10.4171/JFG/156
Publication status	Published - 2025
Externally published	Yes

Keywords

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

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10.4171/JFG/156

Cite this

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title = "Whether p-conductive homogeneity holds depends on p",

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.",

keywords = "Dirichlet form, Mosco convergence, Sierpi{\'n}ski carpets, conductance, energy measure, extension operator, harmonic function, weak convergence",

author = "Shiping Cao and Chen, \{Zhen Qing\}",

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journal = "Journal of Fractal Geometry",

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AU - Chen, Zhen Qing

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AB - 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.

KW - Dirichlet form

KW - Mosco convergence

KW - Sierpiński carpets

KW - conductance

KW - energy measure

KW - extension operator

KW - harmonic function

KW - weak convergence

UR - https://www.scopus.com/pages/publications/105003742255

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DO - 10.4171/JFG/156

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SP - 93

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JF - Journal of Fractal Geometry

IS - 1-2

ER -

Whether p-conductive homogeneity holds depends on p

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Keywords

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