Minimization of the Cheeger constant for Reuleaux polygons
Abstract
In this paper, it is proven that the regular Reuleaux N N -polygon uniquely minimizes the Cheeger constant within the class of all Reuleaux polygons having at most N N sides. Simultaneously, it is shown that the disk polygon centered at the vertices of a regular triangle with side length d d minimizes the perimeter among disk polygons with center parameter d d , thus providing an affirmative response to Bezdek’s conjecture.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Point processes and geometric inequalities
Mathematics and Applications
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 8
- Pages
- 3495–3506
- Publication date
- 5 March 2026
- Language
- EN