Journal d’Analyse Mathématique

, Volume 87, Issue 1, pp 231-263

First online:

New bounds for Kakeya problems

  • NetsHawk KatzAffiliated withDepartment of Mathematics, Washington University Email author 
  • , Terence TaoAffiliated withDepartment of Mathematics, UCLA

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We establish new estimates on the Minkowski and Hausdorff dimensions of Kakeya sets and we obtain new bounds on the Kakeya maximal operator.