Empirical forms of the Petty projection inequality
Abstract
Abstract The Petty projection inequality is a fundamental affine isoperimetric principle for convex sets. It has shaped several directions of research in the convex geometry which forged new connections between projection bodies, centroid bodies, and mixed volume inequalities. We establish several different empirical forms of the Petty projection inequality by re‐examining these key relationships from a stochastic perspective. In particular, we derive sharp extremal inequalities for several multiple‐entry functionals of random convex sets, including mixed projection bodies and mixed volumes.
Fields of Study & Subjects
Point processes and geometric inequalities
Advanced Combinatorial Mathematics
Mathematical Inequalities and Applications
Publication details
- Journal / source
- Proceedings of the London Mathematical Society
- Volume
- 132
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN