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On the Multilinear Restriction and Kakeya conjectures

Jonathan Bennett·Anthony Carbery·Terence Tao
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Abstract

We prove $d$-linear analogues of the classical restriction and Kakeya conjectures in $\R^d$. Our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians, closely related to heat flow. We conclude by giving some applications to the corresponding variable-coefficient problems and the so-called "joints" problem, as well as presenting some $n$-linear analogues for $n<d$.

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Jonathan Bennett, Anthony Carbery, Terence Tao. 2005-09-12. On the Multilinear Restriction and Kakeya conjectures. https://arxiv.org/abs/math/0509262

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