A short proof of the multilinear Kakeya inequality

By Larry Guth. Mathematical Proceedings of the Cambridge Philosophical Society, 2014

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Abstract We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery and Tao.

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Sharp L2 estimates of the Schrödinger maximal function in higher dimensions (2018, methodology): “A key tool we are using in the broad case is the following multilinear refined Strichartz estimate from [13], which is proved using l(2) decoupling, induction on scales and multilinear Kakeya estimates (see [1, 17]).”
On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane (2021, background): “Guth’s proof of the multilinear Kakeya inequality [11] for a very clean example).”
Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015, background): “There is a rather short proof of the case k = n − 1 in [15] that easily extends to the other values of k .”