论文标题
限制Kakeya套装的方向
Restricting directions for Kakeya sets
论文作者
论文摘要
我们证明，Kakeya最大猜想等于$ω$ -Kakeya最大猜想。这完成了[2]的最新结果，其中Keleti和Math {é}证明了Kakeya的猜想等于$ω$ -Kakeya的猜想。此外，我们改善了$ω$ -Kakeya set的Hausdorff尺寸的混凝土限制：对于任何孔中的$ω$ in s N---1中的$Ω$
We prove that the Kakeya maximal conjecture is equivalent to the $Ω$-Kakeya maximal conjecture. This completes a recent result in [2] where Keleti and Math{é} proved that the Kakeya conjecture is equivalent to the $Ω$-Kakeya conjecture. Moreover, we improve concrete bound on the Hausdorff dimension of a $Ω$-Kakeya set : for any Bore set $Ω$ in S n--1 , we prove that if X $\subset$ R n contains for any e $\in$ $Ω$ a unit segment oriented along e then we have dX $\ge$ 6 11 d$Ω$ + 1 where dE denotes the Hausdorff dimension of a set E.
