论文标题
许多功能和测量barycenters的Blaschke-Santalo不平等
Blaschke-Santalo inequality for many functions and geodesic barycenters of measures
论文作者
论文摘要
由最佳运输理论中的大地式barycenter问题激发，我们证明了Blaschke-Santalo不平等的自然概括和许多集合和许多功能的仿射等级不等式。我们源自它的熵结合，用于巴里焦问题中出现的坎托维奇总成本。我们还建立了一个“点式前腿 - 律师不平等”，并显示了多边缘blaschke-santalo功能的单调性能。
Motivated by the geodesic barycenter problem from optimal transportation theory, we prove a natural generalization of the Blaschke-Santalo inequality and the affine isoperimetric inequalities for many sets and many functions. We derive from it an entropy bound for the total Kantorovich cost appearing in the barycenter problem. We also establish a "pointwise Prekopa-Leindler inequality" and show a monotonicity property of the multimarginal Blaschke-Santalo functional.
