Improved Fourier restriction estimates in higher dimensions

  title={Improved Fourier restriction estimates in higher dimensions},
  author={John L. Hickman and Keith M. Rogers},
  journal={Cambridge Journal of Mathematics},
We consider Guth's approach to the Fourier restriction problem via polynomial partitioning. By writing out his induction argument as a recursive algorithm and introducing new geometric information, known as the polynomial Wolff axioms, we obtain improved bounds for the restriction conjecture, particularly in high dimensions. Consequences for the Kakeya conjecture are also considered. 

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