论文标题
Falconer在均匀维度上的距离设置问题的改进结果
An improved result for Falconer's distance set problem in even dimensions
论文作者
论文摘要
我们表明，如果紧凑型设置$ e \ subset \ mathbb {r}^d $具有大于$ \ frac {d} {2} {2}+\ frac {1} {4} $的hausdorff dimension，其中$ d \ geq 4 $甚至是integer，那么$ e $ e $ e $ $ $ $ $ $ $ $ $。这改善了以前最著名的结果，即在偶数方面对Falconer的距离猜想。
We show that if compact set $E\subset \mathbb{R}^d$ has Hausdorff dimension larger than $\frac{d}{2}+\frac{1}{4}$, where $d\geq 4$ is an even integer, then the distance set of $E$ has positive Lebesgue measure. This improves the previously best known result towards Falconer's distance set conjecture in even dimensions.
