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Abstract
A zone of width $ω$ on the unit sphere is the set of points within spherical distance $ω/2$ of a given great circle. We show that the total width of any collection of zones covering the unit sphere is at least $π$, answering a question of Fejes Tóth from 1973.
arXiv comments
10 pages, 3 figures, this version adds some conjectures, accepted to Geom. Funct. Anal., corrections suggested by the referees have been incorporated
Early version of the paper on Arxiv: https://arxiv.org/abs/1703.10550
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