2024/09/03 by Martín, Saúl Rodríguez · 2 citations
#51F99 #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2409.02248
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 \mathbbS1 and the n-dimensional sphere \mathbbSn (for any n∈ℕ) when endowed with their respective geodesic metrics. Additionally, we prove that the GH distance between \mathbbS3 and \mathbbS4 is equal to (1)/(2)\arccos((-1)/(4)), thus settling the case n=3 of a conjecture by Lim, Mémoli and Smith.