4 papers · 1 filter
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…
Metric Topologies on Multiset Spaces as Topological Monoids and Their Group Completion
Donghan Kim
We construct a multiset space over a metric space that simultaneously enjoys desirable topological properties and admits a natural matching metric $d_{\mathbb{N…
Expensive Homeomorphism of Convex Bodies
Donghan Kim
In this paper, we address the longstanding question of whether expansive homeomorphisms can exist within convex bodies in Euclidean spaces. Utilizing fundamental tools from topolog…
Equichordal Points of Convex Bodies
Leo Jang, Donghan Kim
The equichordal point problem is a classical question in geometry, asking whether there exist multiple equichordal points within a single convex body. An equichordal point is defin…