A Nonlinear Variant of Ball's Inequality

TL;DR

This paper introduces a nonlinear variant of Ball's inequality by adapting an induction-on-scales method to establish a stability result for the nonlinear Brascamp-Lieb functional, advancing understanding of these inequalities.

Contribution

It develops a nonlinear version of Ball's inequality using a heat-flow approach, providing new stability insights for the nonlinear Brascamp-Lieb inequalities.

Findings

Established a global near-monotonicity for the nonlinear Brascamp-Lieb functional.

Proved a stability result for the finiteness of nonlinear Brascamp-Lieb inequalities.

Extended the induction-on-scales technique to a nonlinear setting.

Abstract

We adapt an 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 follows a stability result for the finiteness of global nonlinear Brascamp-Lieb inequalities.