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math.MG2026
Gromov-Hausdorff Distances Between Spheres: Asymptotics and Vietoris-Rips Coindex Bounds
Sunhyuk Lim, Facundo Mémoli, Qingsong Wang
For , let be the infimum of the scales at which the Vietoris-Rips simplicial complex of the unit round sphere , equipped with its geodesic met…
math.MG2026
The Gromov-Hausdorff Distance Between Consecutive Spheres
Donghan Kim, Sunhyuk Lim, Facundo Memoli
We determine the Gromov-Hausdorff distance between consecutive unit round spheres equipped with their geodesic metrics. Put the common geodesic dis…
math.MG2026
Metric Geometry of Lebesgue, Wasserstein, and Gromov-Wasserstein Spaces: Submetries, Curvature, and Geodesics
Martin Bauer, Facundo Mémoli, Tom Needham +1
A metric space gives rise to three natural classes of infinite-dimensional metric spaces associated to : -Wasserstein spaces of probability measures on , nonlinear Leb…