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On the multilinear restriction and Kakeya conjectures

Jonathan Bennett School of Mathematics, University of Birmingham Anthony Carbery School of Mathematics, University of Edinburgh Terence Tao Department of Mathematics, University of California

TBD mathscidoc:1701.331973

Acta Mathematica, 196, (2), 261-302, 2005.9
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$n$<$d$.
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@inproceedings{jonathan2005on,
  title={On the multilinear restriction and Kakeya conjectures},
  author={Jonathan Bennett, Anthony Carbery, and Terence Tao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203349301410682},
  booktitle={Acta Mathematica},
  volume={196},
  number={2},
  pages={261-302},
  year={2005},
}
Jonathan Bennett, Anthony Carbery, and Terence Tao. On the multilinear restriction and Kakeya conjectures. 2005. Vol. 196. In Acta Mathematica. pp.261-302. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203349301410682.
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