Blaschke-Santalo inequality for many functions and geodesic barycenters of measures

Alexander V. Kolesnikov, Elisabeth M. Werner

Published 2020-09-30Version 1

Motivated by the geodesic barycenter problem from optimal transportation theory, we prove a natural generalization of the Blaschke-Santalo inequality for many sets and many functions. We derive from it an entropy bound for the total Kantorovich cost appearing in the barycenter problem.