Kakeya set conjecture, all dimensions
Settled for n = 2 (Davies, 1971) and n = 3 (Wang and Zahl, 2025), and over finite fields (Dvir, 2008, with a startlingly short polynomial-method proof). The general Euclidean case is open. It sits under many problems in harmonic analysis, including restriction and Bochner–Riesz.
What would settle it
Lean statement in formal-conjectures
Sources
Relations to this page
- generalizes Kakeya conjecture in three dimensions solved · V3
The original curation records this as a special case of Kakeya set conjecture, all dimensions; the argument for the link has not been written yet.
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