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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.26448 |
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| _version_ | 1866909003152359424 |
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| author | Córdoba, Antonio |
| author_facet | Córdoba, Antonio |
| contents | Let us consider a sphere $S^{n-1}$ of radius $r$ in $\mathbb{R}^n$, where we have fixed poles $N$ and $S$. Suppose that $K$ is a set in $\mathbb{R}^n$ containing a translated copy of each meridian (that is an $S^{n-2}$-sphere) of $S^{n-1}$. Then the Hausdorff dimension of $K$ must be bigger than or equal to $n-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26448 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Hausdorff dimension of sets containing circles in many directions Córdoba, Antonio Metric Geometry 28A75 Let us consider a sphere $S^{n-1}$ of radius $r$ in $\mathbb{R}^n$, where we have fixed poles $N$ and $S$. Suppose that $K$ is a set in $\mathbb{R}^n$ containing a translated copy of each meridian (that is an $S^{n-2}$-sphere) of $S^{n-1}$. Then the Hausdorff dimension of $K$ must be bigger than or equal to $n-1$. |
| title | The Hausdorff dimension of sets containing circles in many directions |
| topic | Metric Geometry 28A75 |
| url | https://arxiv.org/abs/2604.26448 |