On the multilinear restriction and Kakeya conjectures

2006/01/01 by Jonathan Bennett, Anthony Carbery, Terence Tao · 22 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #advanced mathematical theories

paper · pdf · doi:10.1007/s11511-006-0006-4

Abstract

We prove d-linear analogues of the classical restriction and Kakeya conjectures in Rd. 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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