We prove the folklore endpoint multilinear -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 -variety theorem. Finally, we generalize our results to the endpoint perturbed Brascamp–Lieb inequalities using techniques in earlier sections.
"The endpoint perturbed Brascamp–Lieb inequalities with examples." Anal. PDE 11 (3) 555 - 581, 2018. https://doi.org/10.2140/apde.2018.11.555