Type: Article
Publication Date: 2006-01-01
Citations: 333
DOI: https://doi.org/10.1007/s11511-006-0006-4
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.