Acta Mathematica

On the multilinear restriction and Kakeya conjectures

Jonathan Bennett, Anthony Carbery, and Terence Tao

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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.

Article information

Source
Acta Math., Volume 196, Number 2 (2006), 261-302.

Dates
Received: 30 September 2005
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891825

Digital Object Identifier
doi:10.1007/s11511-006-0006-4

Mathematical Reviews number (MathSciNet)
MR2275834

Zentralblatt MATH identifier
1203.42019

Subjects
Primary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Rights
2006 © Institut Mittag-Leffler

Citation

Bennett, Jonathan; Carbery, Anthony; Tao, Terence. On the multilinear restriction and Kakeya conjectures. Acta Math. 196 (2006), no. 2, 261--302. doi:10.1007/s11511-006-0006-4. https://projecteuclid.org/euclid.acta/1485891825


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