The isominwidth problem on the 2‐sphere
Abstract
Abstract 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 . If the width is greater than , 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.
Fields of Study & Subjects
Point processes and geometric inequalities
Advanced Combinatorial Mathematics
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN