Stability for Borell-Brascamp-Lieb inequalities

Abstract

We study stability issues for the so-called Borell-Brascamp-Lieb inequalities, proving that when near equality is realized, the involved functions must be $L^1$-close to be $p$-concave and to coincide up to homotheties of their graphs.

arXiv commentto appear in GAFA Seminar Notes