2025/12/04 by Katherina von Dichter, von Dichter, Katherina, Mia Runge +1
Computer Science · Mathematics · #52A10 #52A40 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2512.04633
openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28
We completely describe the region of possible values of the diameter-width ratio for planar pseudo-complete sets in dependence of the Minkowski asymmetry. In order to do this, we focus on the containment inequalities of K ∩ (-K) and (K-K)/(2) for a Minkowski centered convex compact set K, i.e. we define τ(K) to be the smallest possible factor to cover K ∩ (-K) by a rescalation of (K-K)/(2) and give the region of the possible values of τ(K) in the planar case in dependence of the Minkowski asymmetry of K.