NKBesicovitch
Lean proofs of Hausdorff dimension at least n-(n-k)/p_c^k for all (n,k)-Besicovitch sets with 1 n. Here a Besicovitch set contains a translated unit k-disk in every k-dimensional direction, and p_c is the unique root in (2,3) of p^3-2p^2-2p+2=0. Building on Bourgain's arithmetic-combinatorial approach, Nets Hawk Katz and Terence Tao's New bounds for Kakeya problems (2002; preprint 2001) established the Minkowski-dimension bound 1+(n-1)/beta_c, where beta_c=p_c/(p_c-1)=1.67513... satisfies beta_c^3-4*beta_c+2=0. This is exactly n-(n-1)/p_c, so the numerical exponent itself is not new. They…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-09-19-000001
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-19-000001/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-19-000001/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'