Homogeneous maximizers of the Blaschke--Santalo-type functionals
Abstract
We study Blaschke--Santal{ó}-type inequalities for $N \ge 2$ sets (functions) and a special class of cost functions. In particular, we prove new results about the reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to the homogeneous case (functional inequalities on the sphere) and prove new inequalities for $N>2$ sets by the symmetrization argument. We also discuss the links to the multimagrinal optimal transportation problem and the related sharp transportation-information inequalities.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Mathematical Inequalities and Applications
Point processes and geometric inequalities
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 10 February 2026
- Language
- EN
- Document type
- Preprint