An Algebraic Brascamp-Lieb Inequality

Abstract: The Brascamp-Lieb inequalities are a natural generalisation of many familiar multilinear inequalities that arise in mathematical analysis, classical examples of which include Holder’s inequality, Young’s convolution inequality, and the Loomis-Whitney inequality. Each Brascamp-Lieb inequality is uniquely defined by a 'Brascamp-Lieb datum', which is a pair consisting of a set of linear surjections between euclidean spaces and a set of exponents corresponding to these maps. It is common in applications to encounter nonlinear variants, where the linear maps are replaced with nonlinear maps between manifolds. By incorporating a dampening factor that compensates for local degeneracies, we establish a global nonlinear Brascamp-Lieb inequality for a broad class of maps that exhibit a certain algebraic structure, with a constant that explicitly depends only on the associated 'degrees' of these maps.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.