论文标题
盖盖定理
A cap covering theorem
论文作者
论文摘要
单位$ d $ -sphere $ s $上的球形半径$α$是从球体上给定点的球形距离$α$内的一组点。令$ \ Mathcal F $为$ s $上的有限帽。我们证明，如果没有$ s $的中心的超平面将$ \数学f $划分为两个非空的子集，而不会与$ \ nathcal f $相交任何上限，那么如果$ \ mathcal f $覆盖所有$ \ nathcal f $ us的$ \ m radi的cap cap cap cap cap cap cap等于$ \ mathcal f $ sum $ udi $ radi $ radi的caps cap。 这是Goodman和Goodman涵盖定理的所谓圆圈的球形类似物，也是江斯和作者Arxiv证明的FejesTóth区域的加强：1703.10550。
A cap of spherical radius $α$ on a unit $d$-sphere $S$ is the set of points within spherical distance $α$ from a given point on the sphere. Let $\mathcal F$ be a finite set of caps lying on $S$. We prove that if no hyperplane through the center of $ S $ divides $\mathcal F$ into two non-empty subsets without intersecting any cap in $\mathcal F$, then there is a cap of radius equal to the sum of radii of all caps in $\mathcal F$ covering all caps of $\mathcal F$ provided that the sum of radii is less $π/2$. This is the spherical analog of the so-called Circle Covering Theorem by Goodman and Goodman and the strengthening of Fejes Tóth's zone conjecture proved by Jiang and the author arXiv:1703.10550.
