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[en] A set E ⊂ ℝd whose indicator function 1E has maximal Gowers norm, among all sets of equal measure, is an ellipsoid up to Lebesgue null sets. If 1E has nearly maximal Gowers norm then E nearly coincides with some ellipsoid, in the sense that their symmetric difference has small Lebesgue measure.
Journal
Acta Mathematica Sinica. English Series (Internet); ISSN 1439-7617; 
; v. 35(6); p. 771-782
; v. 35(6); p. 771-782