A Nonlinear Variant of Ball's Inequality

Abstract

We adapt a recent induction-on-scales argument of Bennett, Bez, Buschenhenke, Cowling, and Flock to establish a global near-monotonicity statement for the nonlinear Brascamp-Lieb functional under a certain heat-flow, from which we establish some finiteness and stability results for the associated nonlinear Brascamp-Lieb inequality