2 papers
math.CO2026
Maximum Persistent Betti Numbers of Äech Complexes
Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa
This note proves that only a linear number of holes in a Äech complex of points in can persist over an interval of constant length. Specifically, for any fixed…
cs.CG2025
The Mid-sphere Cousin of the Medial Axis Transform
Herbert Edelsbrunner, Elizabeth Stephenson, Martin Hafskjold Thoresen
The medial axis of a smoothly embedded surface in consists of all points for which the Euclidean distance function on the surface has at least two minima. We general…