论文标题
besicovitch cantor图的Hausdorff尺寸
Hausdorff dimension of Besicovitch sets of Cantor graphs
论文作者
论文摘要
我们考虑平面贝西科维奇的豪斯多夫尺寸，用于可整流设置$γ$，即每个方向都包含$γ$的旋转副本。我们表明，对于大型的Cantor套装$ c $和cantor-graphs $γ$构建的$ c $，任何$γ$ -Besicovitch set的Hausdorff尺寸必须至少为$ \ min \ left（2-s^2，\ frac {1}} {1} {s} {s} {s} {s} {s} {s} {s} {s} {s} \ right）$ c $。
We consider the Hausdorff dimension of planar Besicovitch sets for rectifiable sets $Γ$, i.e. sets that contain a rotated copy of $Γ$ in each direction. We show that for a large class of Cantor sets $C$ and Cantor-graphs $Γ$ built on $C$, the Hausdorff dimension of any $Γ$-Besicovitch set must be at least $\min\left(2-s^2,\frac{1}{s}\right)$, where $s=\dim C$.
