Pál's isominwidth inequality for ball convex bodies in planes of constant curvature
Abstract
Pál's classical isominwidth inequality states that the regular triangle has minimal area among plane convex bodies of minimal width $w$. A similar result is the Blaschke--Lebesgue inequality that states that Reuleaux triangles minimize the area among bodies of constant width $w$ in the plane. In this paper, we connect these two problems by solving the isominwidth problem for $r$-ball convex bodies in the Euclidean, hyperbolic and spherical planes.
Fields of Study & Subjects
Point processes and geometric inequalities
Advanced Combinatorial Mathematics
Mathematics and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 22 February 2026
- Language
- EN
- Document type
- Preprint