Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914267194720256 |
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| author | Anttila, Riku Eriksson-Bique, Sylvester Rainio, Lassi |
| author_facet | Anttila, Riku Eriksson-Bique, Sylvester Rainio, Lassi |
| contents | A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfors regular conformal dimension of a symmetric Laakso-type fractal space is attained. The attaining metrics are constructed explicitly. This gives new examples of attainment and clarifies the possible obstructions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_14241 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conformal dimension and its attainment on self-similar Laakso-type fractal spaces Anttila, Riku Eriksson-Bique, Sylvester Rainio, Lassi Metric Geometry 30L10, 53C23, 20F65, 51F99, 28A78 A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfors regular conformal dimension of a symmetric Laakso-type fractal space is attained. The attaining metrics are constructed explicitly. This gives new examples of attainment and clarifies the possible obstructions. |
| title | Conformal dimension and its attainment on self-similar Laakso-type fractal spaces |
| topic | Metric Geometry 30L10, 53C23, 20F65, 51F99, 28A78 |
| url | https://arxiv.org/abs/2601.14241 |