Proof of László Fejes Tóth’s zone conjecture


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.

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Corresponding author

Correspondence to Zilin Jiang.

Additional information

Z. Jiang was supported in part by ISF Grant Nos. 1162/15, 936/16.

A. Polyanskii was supported in part by ISF Grant No. 409/16, and by the Russian Foundation for Basic Research through Grant Nos. 15-01-99563 A, 15-01-03530 A. The work was done when A. Polyanskii was a postdoctoral fellow at the Technion.

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Jiang, Z., Polyanskii, A. Proof of László Fejes Tóth’s zone conjecture. Geom. Funct. Anal. 27, 1367–1377 (2017).

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