New Kakeya estimates using Gromov's algebraic lemma

DOI10.1016/j.aim.2021.107596zbMath1459.42032arXiv1908.05314OpenAlexW3125619394WikidataQ124853457 ScholiaQ124853457MaRDI QIDQ2227287

Joshua Zahl

Publication date: 15 February 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.05314

zbMATH Keywords

Besicovitch setreal algebraic geometryKakeya problem

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Semialgebraic sets and related spaces (14P10)

Related Items (6)

A note on local smoothing estimates for fractional Schrödinger equations ⋮ The 𝑝-adic Kakeya conjecture ⋮ The Kakeya conjecture on local fields of positive characteristic ⋮ An improved bilinear restriction estimate for the paraboloid in \(\mathbb{R}^3\) ⋮ Unnamed Item ⋮ Tomography bounds for the Fourier extension operator and applications

Cites Work

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• On the Erdős distinct distances problem in the plane
• The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture
• Bounds on oscillatory integral operators based on multilinear estimates
• On the multilinear restriction and Kakeya conjectures
• A proof of Yomdin-Gromov's algebraic Lemma
• Volumes of tubular neighbourhoods of real algebraic varieties
• Restriction estimates using polynomial partitioning. II
• On the polynomial Wolff axioms
• Recent progress on the Kakeya conjecture
• An improved bound for Kakeya type maximal functions
• The endpoint multilinear Kakeya theorem via the Borsuk-Ulam theorem
• A Kakeya maximal function estimate in four dimensions using planebrushes
• Improved Fourier restriction estimates in higher dimensions
• A discretized Severi-type theorem with applications to harmonic analysis
• A restriction estimate using polynomial partitioning
• The Kakeya Maximal Function and the Spherical Summation Multipliers
• Polynomial Wolff axioms and Kakeya-type estimates in R4
• On the number of cells defined by a family of polynomials on a variety
• An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³
• On the Betti Numbers of Real Varieties

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