Two-scale Kakeya upper Minkowski lower bound
We prove that every bounded Kakeya set in Rⁿ, n ≥ 4, has upper Minkowski dimension at least 0.597n. Here a Kakeya set contains a unit line segment in every direction. This improves the asymptotic coefficient c_KT = 1/α = 0.596968283237… in the Katz–Tao bound 1 + c_KT(n−1), where α is the unique root of α³−4α+2 = 0 in (1,2). The proof combines arithmetic estimates for line segments with geometric estimates for tubes at two different widths.
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-10-21-000006
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-21-000006/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-21-000006/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'