Ferenc Fodor: On Liakopoulos's dual Bollobás--Thomason inequality скачать в хорошем качестве

Ferenc Fodor: On Liakopoulos's dual Bollobás--Thomason inequality

(12 décembre 2025/ December 12, 2025) Colloque des sciences mathématiques du Québec/CSMQ https://www.crmath.ca/en/activities/#... Ferenc Fodor (Bolyai Institute, University of Szeged): On Liakopoulos's dual Bollobás--Thomason inequality Abstract: The Loomis--Whitney (1949) inequality provides an upper bound for the volume of a convex body via projections to the coordinate hyperplanes. Meyer (1988) proved a lower bound using intersections with the same coordinate hyperplanes. Equality is characterized in both cases. The Bollobás--Thomason (1995) inequality is a generalization of the Loomis-Whitney inequality that uses projections to a system of certain subspaces spanned by standard basis vectors. Liakopoulos (2019) proved a quite general dual statement giving a lower bound for the volume based on products of intersection volumes with certain systems of subspaces. We characterize equality of Liakopoulos's inequality via Barthe's Reverse Geometric Brascamp--Lieb inequality. Joint work with K.J. Böröczky (Alfr\'ed Rényi Institute of Mathematics, Hungary) and P. Kalantzopoulos (University of Waterloo).