7 papers
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…
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…
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…
Super-Polynomial Growth of the Generalized Persistence Diagram
Donghan Kim, Woojin Kim, Wonjun Lee
The Generalized Persistence Diagram (GPD) for multi-parameter persistence naturally extends the classical notion of persistence diagram for one-parameter persistence. However, unli…
On isomorphism of the space of continuous functions with finite -th variation along a partition sequence
Purba Das, Donghan Kim
We study the concept of (generalized) -th variation of a real-valued continuous function along a general class of refining sequence of partitions. We show that the finiteness of…