Flow methods in geometric aspects of harmonic analysis.

这是欧几里得调和分析的一个项目，主要研究流动方法在多线性泛函不等式中的应用。这些方法在谐波分析中的适用性在过去的5-10年里出现了意想不到的激增，在偏微分方程和数论等领域产生了重要影响。本项目的目的是在与傅里叶变换的多线性限制理论相关的各种情况下改进这些方法。更具体地说，该项目旨在获得所谓的非线性Brascamp-Lieb泛函的近单调性陈述，并探索其对非线性Brascamp-Lieb不等式的影响。

This is a project in Euclidean Harmonic Analysis focussing on the application of flow methods in the context of multilinear functional inequalities. The applicability of such methods in harmonic analysis has seen an unexpected surge over the last 5-10 years, with important consequences in areas such as partial differential equations and number theory. The purpose of this project is to refine these methods in various contexts related to the multilinear restriction theory of the Fourier transform. More specifically, the project aims to obtain near-monotonicity statements for the so-called nonlinear Brascamp-Lieb functional, and explore its consequences for the nonlinear Brascamp-Lieb inequality.