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.
Citation
Jonathan Bennett. Anthony Carbery. Terence Tao. "On the multilinear restriction and Kakeya conjectures." Acta Math. 196 (2) 261 - 302, 2006. https://doi.org/10.1007/s11511-006-0006-4
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