Back to Search
Start Over
Some novel constructions of optimal Gromov-Hausdorff-optimal correspondences between spheres
- Publication Year :
- 2024
-
Abstract
- 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, M\'emoli and Smith.
- Subjects :
- Mathematics - Metric Geometry
51F99
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.02248
- Document Type :
- Working Paper