2024/11/18 by Ansgar Freyer, Freyer, Ansgar, Ádám Sagmeister +1
Computer Science · Engineering · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.2411.11462
openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pál's isominwidth theorem states that for a fixed minimal width, the regular triangle has minimal area. A spherical version of this theorem was proven by Bezdek and Blekherman, if the minimal width is at most \tfrac π2. If the width is greater than \tfrac π2, the regular triangle no longer minimizes the area at fixed minimal width. We show that the minimizers are instead given by the polar sets of spherical Reuleaux triangles. Moreover, stability versions of the two spherical inequalities are obtained.