Variants of a theorem of Macbeath in finite‐dimensional normed spaces
Abstract
Abstract A classical theorem of Macbeath states that for any integers , , ‐dimensional Euclidean balls are hardest to approximate, in terms of volume difference, by inscribed convex polytopes with vertices. In this paper, we investigate normed variants of this problem: we intend to find the extremal values of the Busemann volume, Holmes–Thompson volume, Gromov's mass, and Gromov's of a largest volume convex polytope with vertices, inscribed in the unit ball of a ‐dimensional normed space.
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
- 2
- Publication date
- 10 February 2026
- Language
- EN