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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.01953 |
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| _version_ | 1866917581435174912 |
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| author | Cao, Shiping Chen, Zhen-Qing |
| author_facet | Cao, Shiping Chen, Zhen-Qing |
| contents | We introduce two fractals, in Euclidean spaces of dimension two and three respectively, such the $2$-conductive homogeneity holds but there is some $\eps \in (0, 1)$ so that the $p$-conductive homogeneity fails for every $p\in (1, 1+\eps)$. In addition, these two fractals have Ahlfors regular conformal dimension within the interval $(1, 2)$ and $(2, 3)$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Whether $p$-conductive homogeneity holds depends on $p$ Cao, Shiping Chen, Zhen-Qing Functional Analysis 31E05 We introduce two fractals, in Euclidean spaces of dimension two and three respectively, such the $2$-conductive homogeneity holds but there is some $\eps \in (0, 1)$ so that the $p$-conductive homogeneity fails for every $p\in (1, 1+\eps)$. In addition, these two fractals have Ahlfors regular conformal dimension within the interval $(1, 2)$ and $(2, 3)$, respectively. |
| title | Whether $p$-conductive homogeneity holds depends on $p$ |
| topic | Functional Analysis 31E05 |
| url | https://arxiv.org/abs/2402.01953 |