The logarithmic Brunn-Minkowski conjecture

Orateur: Alexandros ESKENAZIS
Localisation: Université de Cambridge, Royaume-Uni
Type: Séminaire informel analyse
Site: UGE
Date de début: 18/05/2021 - 10:30
Date de fin: 18/05/2021 - 12:00

We shall discuss the conjectured logarithmic Brunn-Minkowski inequality of Böröczky, Lutwak, Yang and Zhang (2012), which is a far-reaching refinement of the classical Brunn-Minkowski inequality for symmetric convex sets. After a quick recap of known special cases, we will explain an equivalent local form of the conjecture which is a functional inequality for functions defined on the boundary of symmetric convex sets. Time permitting, we will then show the solution (from joint work with G. Moschidis) of the Gardner-Zvavitch problem, which is formally weaker than the log-Brunn-Minkowski inequality.