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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.GT2026
Proper Homotopy Nonrigidity of Open Contractible Manifolds
Donghan Kim
We study whether proper homotopy equivalence classifies open contractible manifolds arising as interiors of compact contractible manifolds. In dimensions three and four, it does: a…