Marius Tiba King's College London

Sharp stability of the Brunn–Minkowski, Prékopa–Leindler and Borell–Brascamp–Lieb inequalities

Abstract:

The Borell–Brascamp–Lieb inequality is a generalization of the Prékopa–Leindler inequality which in turn is a functional extension of the Brunn–Minkowski inequality, which further implies the classical isoperimetric inequality. The study of these fundamental geometric inequalities and their stability has a rich history. We prove a sharp stability result for the Brunn–Minkowski, Prékopa–Leindler and Borell–Brascamp–Lieb inequalities thus concluding a long line of research on this problem. This is joint work with Alessio Figalli and Peter van Hintum.