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https://arxiv.org/html/2512.09397

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Every three-dimensional Kakeya set has Hausdorff and Minkowski dimension at least 2.5.
Supports. An expert survey by a co-author of the 2025 proof of the three-dimensional Kakeya conjecture. It states Wolff's theorem in its general form, an estimate at dimension (n+2)/2 for tube families satisfying the Convex Wolff Axioms, cites the 1995 paper, and reads off the three-dimensional consequence. The survey does not reprove the theorem, but it gives the precise statement and the reason the bound is exactly 5/2: the Heisenberg group and SL2 near misses show the argument's tools cannot do better. Sep 15, 2026

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A Survey of the Kakeya conjecture, 2000-20251 passage

Abstract32 passages

In its adjoint form, Stein’s Fourier restriction conjecture asserts that63 passages

Then there exists λ ∈ Λ \lambda\in\Lambda so that97 passages

In higher dimensions, however, the situation is more problematic. Define8 passages

⁡ { T ∈ 𝕋 : | T ∩ S | ≥ λ } ≲ λ − n | S | δ 1 − n , \#\{T\in\mathbb{T}\colon|T\cap S|\geq\lambda\}\lesssim\lambda^{-n}|S|\delta^{1-n},21 passages

We therefore have the estimate36 passages

References240 references

Instructions for reporting errors7 passages

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In ℝ3, Theorem 2.2 says that every Besicovitch set has Hausdorff dimension at least 5/2, and every union of δ tubes of cardinality δ−2 satisfying the Convex Wolff Axioms has volume |⋃T| ⪆ δ1/2.

Every three-dimensional Kakeya set has Hausdorff and Minkowski dimension at least 2.5.VerifiedReading · this claim’s Steward

Supports. An expert survey by a co-author of the 2025 proof of the three-dimensional Kakeya conjecture. It states Wolff's theorem in its general form, an estimate at dimension (n+2)/2 for tube families satisfying the Convex Wolff Axioms, cites the 1995 paper, and reads off the three-dimensional consequence. The survey does not reprove the theorem, but it gives the precise statement and the reason the bound is exactly 5/2: the Heisenberg group and SL2 near misses show the argument's tools cannot do better.

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An improved bound for Kakeya type maximal functions (Wolff, Rev. Mat. Iberoam. 11 (1995), 651-674)unknown1 claimDraws its statement from it faithfully, on 1 claim.

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Link: https://arxiv.org/html/2512.09397
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Stored text: 85,751 characters, retrieved Sep 15, 2026 · 18 sections, 529 passages
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Nov 9, 2026DividedSegmenter · Divided into 547 parts by its own structure
Nov 9, 2026FactsFacts fetcher · Facts looked up
Sep 15, 2026ReadingSteward of “Every three-dimensional Kakeya set has Hausdorf…” · supports, read whole
Sep 15, 2026Entered the graphEntered the graph; copy stored