Quasisymmetric mappings on two variants of fractal percolation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916996427284480 |
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| author | Anttila, Roope Eriksson-Bique, Sylvester Pyörälä, Aleksi |
| author_facet | Anttila, Roope Eriksson-Bique, Sylvester Pyörälä, Aleksi |
| contents | We study quasisymmetric maps on two variants of the classical fractal percolation model: the fat and dense fractal percolations. We show that, almost surely conditioned on non-extinction, the Hausdorff dimension of the fat fractal percolation cannot be lowered with a quasisymmetry and the Hausdorff dimension of the dense fractal percolation cannot be lowered with a power quasisymmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasisymmetric mappings on two variants of fractal percolation Anttila, Roope Eriksson-Bique, Sylvester Pyörälä, Aleksi Metric Geometry Probability 30L10, 28A80, 60D05 We study quasisymmetric maps on two variants of the classical fractal percolation model: the fat and dense fractal percolations. We show that, almost surely conditioned on non-extinction, the Hausdorff dimension of the fat fractal percolation cannot be lowered with a quasisymmetry and the Hausdorff dimension of the dense fractal percolation cannot be lowered with a power quasisymmetry. |
| title | Quasisymmetric mappings on two variants of fractal percolation |
| topic | Metric Geometry Probability 30L10, 28A80, 60D05 |
| url | https://arxiv.org/abs/2510.06900 |