English

Proof of L\'aszl\'o Fejes T\'oth's zone conjecture

Metric Geometry 2017-12-20 v2 Combinatorics

Abstract

A zone of width ω\omega on the unit sphere is the set of points within spherical distance ω/2\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 π\pi, answering a question of Fejes T\'oth from 1973.

Keywords

Cite

@article{arxiv.1703.10550,
  title  = {Proof of L\'aszl\'o Fejes T\'oth's zone conjecture},
  author = {Zilin Jiang and Alexandr Polyanskii},
  journal= {arXiv preprint arXiv:1703.10550},
  year   = {2017}
}

Comments

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