#### Vol. 11, No. 3, 2018

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The endpoint perturbed Brascamp–Lieb inequalities with examples

### Ruixiang Zhang

Vol. 11 (2018), No. 3, 555–581
##### Abstract

We prove the folklore endpoint multilinear ${k}_{j}$-plane conjecture originating in a paper of Bennett, Carbery and Tao where the almost sharp multilinear Kakeya estimate was proved. Along the way we prove a more general result, namely the endpoint multilinear ${k}_{j}$-variety theorem. Finally, we generalize our results to the endpoint perturbed Brascamp–Lieb inequalities using techniques in earlier sections.

##### Keywords
Brascamp–Lieb inequality, polynomial method
Primary: 42B10