Limits RegistryPUBLIC RECORD
Limits RegistryHong Wang (NYU) and Joshua Zahl (University of British Columbia) posted a proof in February 2025 that Kakeya sets in three-dimensional space must have full dimension 3, resolving a central open problem in harmonic analysis. The plane case was settled by Roy Davies in 1971; the conjecture remains open in four or more dimensions.
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Hong Wang (NYU) and Joshua Zahl (University of British Columbia) posted a proof in February 2025 that Kakeya sets in three-dimensional space must have full dimension 3, resolving a central open problem in harmonic analysis. The plane case was settled by Roy Davies in 1971; the conjecture remains open in four or more dimensions.
Every Kakeya set in R^3 (a compact set containing a unit line segment in every direction) has Hausdorff and Minkowski dimension 3.
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Limits Registry. LR-KAKEYA-CONJECTURE-THREE-DIMENSIONS. Kakeya set conjecture proved in three dimensions. 2026.