关于欧几里得空间中域的阴影问题
On the shadow problem for domains in the Euclidean spaces
摘要：
本文研究了在空间域$\mathbb{R}^n$，$n\le 3$上推广的阴影问题.这里的阴影问题是指找到满足某些条件的最小数量的球，使得通过给定点的每条线至少与集合中的一个球相交。证明了在空间$\mathbb{R}^3$（$\mathbb{R}^2$）的任意定义域的任意给定点上，用互不重叠的不保持该点的闭球或开球的集合生成阴影，只要有四个球就足够了.
英文摘要：
In the present work, the problem about shadow, generalized on domains of space $\mathbb{R}^n$, $n\le 3$, is investigated. Here the shadow problem means to find the minimal number of balls satisfying some conditions an such that every line passing through the given point intersects at least one ball of the collection. It is proved that to generate the shadow at every given point of any domain of the space $\mathbb{R}^3$ ($\mathbb{R}^2$) with collection of mutually non-overlapping closed or open balls which do not hold the point and with centers on the boundary of the domain, it is sufficient to have four balls.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
