On the Multilinear Restriction and Kakeya conjectures

Details On the Multilinear Restriction and Kakeya conjectures On the Multilinear Restriction and Kakeya conjectures

2005-09-12

arxiv.org/abs/math/0509262v1

Mathematics

Classical Analysis and ODEs

38 pages, no figures, submitted

Scientific paper

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

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