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The cylindrical width of transitive sets

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Abstract

We show that for every 1 ≤ k ≤ d/(log d)C, for some absolute constant C, that every finite transitive set of unit vectors in ℝd lies within distance \(O\left({1/\sqrt {\log \left({d/k} \right)}} \right)\) of some codimension k subspace, and this distance bound is best possible. This extends a result of Ben Green, who proved it for k = 1.

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Ashwin Sah, Mehtaab Sawhney & Yufei Zhao

Authors
  1. Ashwin Sah
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  2. Mehtaab Sawhney
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  3. Yufei Zhao
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Corresponding author

Correspondence to Yufei Zhao.

Additional information

Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-1745302.

Zhao was supported by NSF Award DMS-1764176, a Sloan Research Fellowship, and the MIT Solomon Buchsbaum Fund.

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Sah, A., Sawhney, M. & Zhao, Y. The cylindrical width of transitive sets. Isr. J. Math. 253, 647–672 (2023). https://doi.org/10.1007/s11856-022-2376-5

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  • DOI: https://doi.org/10.1007/s11856-022-2376-5

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