Proof of László Fejes Tóth's zone conjecture

Abstract

A zone of width $\omega$ on the unit sphere is the set of points within spherical distance $\omega /2$ of a given great circle. We show that the total width of any collection of zones covering the unit sphere is at least $\pi$, answering a question of Fejes Tóth from 1973.

10 pages, 3 figures, this version adds some conjectures, accepted to Geom. Funct. Anal., corrections suggested by the referees have been incorporated

Cited by in corpus (4)

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• Extensions of polynomial plank covering theorems
• On the multiplicity of arrangements of congruent zones on the sphere