An Algebraic Brascamp-Lieb Inequality

Abstract

We prove a global nonlinear Brascamp-Lieb inequality for a general class of maps, encompassing polynomial and rational maps, as a consequence of the multilinear Kakeya-type inequalities of Zhang and Zorin-Kranich. We incorporate a natural affine-invariant weight that compensates for local degeneracies, and yields a uniform constant that depends only on the 'degree' of the maps involved.