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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.23057 |
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| _version_ | 1866913865829187584 |
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| author | Kigami, Jun Ota, Yuka |
| author_facet | Kigami, Jun Ota, Yuka |
| contents | We provide a rich family of self-similar sets, called locally symmetric polygon-based self-similar sets, as examples of metric spaces having conductive homogeneity, which was introduced as a sufficient condition for the construction of counterparts of "Sobolev spaces" on compact metric spaces. In particular, our results imply the existence of "Brownian motions" on our family of self-similar sets at the same time. Unlike the known examples like the Sierpinski carpet by Barlow-Bass, unconstrained carpet by Cao and Qiu and the Octa-carpet by Andrews, our examples may have no global symmetries, i.e. the group of isometries is trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conductive homogeneity of locally symmetric polygon-based self-similar sets Kigami, Jun Ota, Yuka Metric Geometry We provide a rich family of self-similar sets, called locally symmetric polygon-based self-similar sets, as examples of metric spaces having conductive homogeneity, which was introduced as a sufficient condition for the construction of counterparts of "Sobolev spaces" on compact metric spaces. In particular, our results imply the existence of "Brownian motions" on our family of self-similar sets at the same time. Unlike the known examples like the Sierpinski carpet by Barlow-Bass, unconstrained carpet by Cao and Qiu and the Octa-carpet by Andrews, our examples may have no global symmetries, i.e. the group of isometries is trivial. |
| title | Conductive homogeneity of locally symmetric polygon-based self-similar sets |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2505.23057 |