Improved Fourier restriction estimates in higher dimensions
By J. Hickman, Keith McKenzie Rogers. Cambridge Journal of Mathematics, 2018
51 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/92f6cde98d3bb77cb87dcd761b89f65b6736bb8c
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In Applied Mathematics
- J. Hickman
- Marina Iliopoulou
- Larry Guth
- Keith McKenzie Rogers
- Xiumin Du
- Ruixiang Zhang
- Jean Bourgain
- F. C. Marques
In Mathematical Physics
- J. Hickman
- Marina Iliopoulou
- Larry Guth
- Keith McKenzie Rogers
- Xiumin Du
- Ruixiang Zhang
- Jean Bourgain
- Ciprian Demeter
Citations in the corpus
- Sharp estimates for oscillatory integral operators via polynomial partitioning (2017, background): “Relaxing L2 to L∞ has led to further improvements on the Fourier restriction problem for the paraboloid [33], [16].”