论文标题
凸面相交的奇异性数量翻译
The Number of Singularities in the Intersections of Convex Planar Translates
论文作者
论文摘要
本文的这一目的是证明以下结果：如果PHI的N翻译的交叉点具有非空的内部，那么让PHI成为欧几里得平面中严格的，光滑的凸面体，并且所有翻译都会有助于交叉点，那么这些n翻译的交叉点将具有沿其sinkularity沿其边界的n点的n点。此外，从某种意义上说，删除我们陈述中的任何一个假设都将使结果总体上无法保持。
This purpose of this paper is to prove the following result: let phi be a strictly convex, smooth, convex body in the Euclidean plane, if the intersection of n translates of phi has a non-empty interior, and all of the translates contribute to the intersection, then the intersection of these n translates will have exactly n points of singularity along its boundary. Furthermore this result is sharp, in the sense that, removing any one of the assumptions from our statement will render the result unable to hold in general.
