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New Kakeya estimates using the polynomial Wolff axioms

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arxiv 1901.01802 v1 pith:ZNQKCAOL submitted 2019-01-07 math.CA math.MG

Jonathan Hickman , Keith M Rogers This is my paper · ORCID
classification math.CAmath.MG
keywords conjecturekakeyaaxiomsboundsestimatesformulationimprovedmaximal
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abstract

We obtain new bounds for the Kakeya maximal conjecture in most dimensions $n<100$, as well as improved bounds for the Kakeya set conjecture when $n=7$ or $9$. For this we consider Guth and Zahl's strengthened formulation of the maximal conjecture, concerning families of tubes that satisfy the polynomial Wolff axioms. Our results give improved estimates for this strengthened formulation when $n =5$ or $n \geq 7$.

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  1. New Kakeya estimates using Gromov's algebraic lemma

    math.CA 2019-08 accept novelty 8.0 of 10

    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.

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