• Corpus ID: 231718845

The cylindrical width of transitive sets

  title={The cylindrical width of transitive sets},
  author={Ashwin Sah and Mehtaab Sawhney and Yufei Zhao},
The following counterintuitive fact was conjectured by the third author and proved by Green [4]. It says that every finite transitive subset of a high dimensional sphere is close to some hyperplane. Here a subset X of a sphere in Rd is transitive if for every x, x′ ∈ X, there is some g ∈ O(Rd) so that gX = X and gx = x′. We say that X has width at most 2r if it lies within distance r of some hyperplane. The finiteness assumption is important since otherwise the whole sphere is a counterexample. 


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