论文标题
在埃德斯的旧定理上关于模棱两可的基因座
On an old theorem of Erdös about ambiguous locus
论文作者
论文摘要
埃尔多斯（Erdös）在1946年证明，如果一套$ e \ subset \ mathbb {r}^n $是封闭且非空的，则在$ \ m m mathbb {r}^n $中的点，称为模棱两可的基因座或内侧轴，与$ e $最接近的属性属于$ e $的属性，n n n n n n n n n n n n n.我们通过在凸度和$ c^2 $规律性方面获得新的规律性结果来改善结果。
Erdös proved in 1946 that if a set $E\subset\mathbb{R}^n$ is closed and non-empty, then the set, called ambiguous locus or medial axis, of points in $\mathbb{R}^n$ with the property that the nearest point in $E$ is not unique, can be covered by countably many surfaces, each of finite $(n-1)$-dimensional measure. We improve the result by obtaining a new regularity result for these surfaces in terms of convexity and $C^2$ regularity.
