Auttawich Manui - On the volume of Minkowski sums of anti-blocking bodies

In this talk, we will explore inequalities related to the volume of Minkowski sums within a specific class of convex bodies known as anti-blocking bodies. We will present analogs of the Plunnecke-Ruzsa-type inequality and the V. Milman inequality, focusing on the concavity of the ratio of volumes of bodies and their projections. If time permits, we will also discuss the counterparts of these results in the context of Firey sums and extend the discussion to cases involving unconditional product measures.

Joint work with Cheikh Saliou Ndiaye (Gustave Eiffel University) and Artem Zvavitch (Kent State).