This paper proves new Kakeya maximal function estimates in R^n at dimension d(n) = max_k min(n-k+2, (n^2+k^2+n-k)/(2n)), improving the previous record in all dimensions n >= 5 except n = 6.
A note on Fourier restriction and nested Polynomial Wolff axioms
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abstract
This note records an asymptotic improvement on the known $L^p$ range for the Fourier restriction conjecture in high dimensions. This is obtained by combining Guth's polynomial partitioning method with recent geometric results regarding intersections of tubes with nested families of varieties.
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New Kakeya estimates using Gromov's algebraic lemma
This paper proves new Kakeya maximal function estimates in R^n at dimension d(n) = max_k min(n-k+2, (n^2+k^2+n-k)/(2n)), improving the previous record in all dimensions n >= 5 except n = 6.