Some novel constructions of optimal Gromov-Hausdorff-optimal correspondences between spheres
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910126491828224 |
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| author | Martín, Saúl Rodríguez |
| author_facet | Martín, Saúl Rodríguez |
| contents | In this article, as a first contribution, we provide alternative proofs of recent results by Harrison and Jeffs which determine the precise value of the Gromov-Hausdorff (GH) distance between the circle $\mathbb{S}^1$ and the $n$-dimensional sphere $\mathbb{S}^n$ (for any $n\in\mathbb{N}$) when endowed with their respective geodesic metrics. Additionally, we prove that the GH distance between $\mathbb{S}^3$ and $\mathbb{S}^4$ is equal to $\frac{1}{2}\arccos\left(\frac{-1}{4}\right)$, thus settling the case $n=3$ of a conjecture by Lim, Mémoli and Smith. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some novel constructions of optimal Gromov-Hausdorff-optimal correspondences between spheres Martín, Saúl Rodríguez Metric Geometry 51F99 In this article, as a first contribution, we provide alternative proofs of recent results by Harrison and Jeffs which determine the precise value of the Gromov-Hausdorff (GH) distance between the circle $\mathbb{S}^1$ and the $n$-dimensional sphere $\mathbb{S}^n$ (for any $n\in\mathbb{N}$) when endowed with their respective geodesic metrics. Additionally, we prove that the GH distance between $\mathbb{S}^3$ and $\mathbb{S}^4$ is equal to $\frac{1}{2}\arccos\left(\frac{-1}{4}\right)$, thus settling the case $n=3$ of a conjecture by Lim, Mémoli and Smith. |
| title | Some novel constructions of optimal Gromov-Hausdorff-optimal correspondences between spheres |
| topic | Metric Geometry 51F99 |
| url | https://arxiv.org/abs/2409.02248 |