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Subsets of Euclidean Space with Nearly Maximal Gowers Norms

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA, 94720-3840, USA

    Michael Christ

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  1. Michael Christ
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Correspondence to Michael Christ.

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Research supported in part by NSF (Grant DMS-1363324)

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Christ, M. Subsets of Euclidean Space with Nearly Maximal Gowers Norms. Acta. Math. Sin.-English Ser. 35, 771–782 (2019). https://doi.org/10.1007/s10114-019-8411-8

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  • DOI: https://doi.org/10.1007/s10114-019-8411-8

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