Degree reduction and graininess for Kakeya-type sets in \(\mathbb{R}^3\)

DOI10.4171/RMI/891zbMath1358.52011arXiv1402.0518OpenAlexW2963754370MaRDI QIDQ726764

Lawrence Guth

Publication date: 14 July 2016

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0518

zbMATH Keywords

incidence geometryKakeya setpolynomial methodcylindrical tubes

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Other problems of combinatorial convexity (52A37) Helly-type theorems and geometric transversal theory (52A35)

Related Items (6)

The endpoint perturbed Brascamp-Lieb inequalities with examples ⋮ Incidence bounds on multijoints and generic joints ⋮ Polynomials with dense zero sets and discrete models of the Kakeya conjecture and the Furstenberg set problem ⋮ Unnamed Item ⋮ A restriction estimate using polynomial partitioning ⋮ An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³

Cites Work

• Unnamed Item
• The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture
• On the multilinear restriction and Kakeya conjectures
• On the dimension of Kakeya sets and related maximal inequalities
• An improved bound on the Minkowski dimension of Besicovitch sets in \(\mathbb{R}^3\)
• Algebraic methods in discrete analogs of the Kakeya problem
• On lines, joints, and incidences in three dimensions
• On the size of Kakeya sets in finite fields

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