Billiard analogue of Blaschke-Santalo inequality

Speaker. Daniel Tsodikovich
Date. 05.12.23 at 14:30

Abstract. The Blaschke-Santalo inequality is a classical inequality in convex geometry. This inequality is about the product of the volumes of a convex body and its dual. In this talk we investigate an analogue of this inequality, where the volume is replaced with the length of the shortest billiard trajectory. We focus on the two dimensional case. We will describe what the analogue of the “Santalo point” is in this setting, show an analogue of the inequality itself, and discuss maximizers in classes of polygons.