Abstract: A cap of spherical radius $\alpha$ on a unit $2$-sphere $S$ is the set of points within spherical distance $\alpha$ from a given point on the sphere. Let $\mathcal S$ be a finite set of caps lying on $S$. We prove that if there is no great circle non-intersecting caps of $\mathcal S$ and dividing $\mathcal S$ into two non-empty subsets, then there is a cap of radius equal to the total radius of caps of $\mathcal S$ covering all caps of $\mathcal S$ provided that the total radius is less $\pi/2$.
This is the spherical analog of the so-called Circle Covering Theorem by Goodman and Goodman and the strengthening of Fejes Toth's zone conjecture proved by Jiang and the author arXiv:1703.10550.
Publication Year: 2020
Publication Date: 2020-06-03
Language: en
Type: preprint
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