Flow methods in geometric aspects of harmonic analysis.

调和分析几何方面的流动方法。

• 批准号: 1935855
• 金额: --
• 依托单位: University of Birmingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1935855
• 关键词: Flow; methods; geometric; aspects; harmonic

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.

这是欧几里德调和分析中的一个项目，重点是在多线性函数不等式的背景下应用流方法。在过去的5-10年里，这种方法在谐波分析中的适用性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。这个项目的目的是完善这些方法在各种背景下有关的多线性限制理论的傅立叶变换。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。