Quantitative stability for sumsets in R[superscript n]
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1412.7586.pdf
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Author(s)
Figalli, Alessio
Jerison, David S
Date Issued
May 2015
Journal
Journal of the European Mathematical Society
Publisher
European Mathematical Publishing House
Citation
Figalli, Alessio, and David Jerison. “Quantitative Stability for Sumsets in R[superscript n].” Journal of the European Mathematical Society, vol. 17, no. 5, 2015, pp. 1079–106.
Version
Author's final manuscript
Abstract
Given a measurable set A ⊂ ℝ[superscript n] of positive measure, it is not difficult to show that |A + A| = |2A| if and only if A is equal to its convex hull minus a set of measure zero. We investigate the stability of this statement: If (|A + A| - |2A|)/|A| is small, is A close to its convex hull? Our main result is an explicit control, in arbitrary dimension, on the measure of the difference between A and its convex hull in terms of (|A + A| - |2A|)/|A|. Keywords: Quantitative stability, sumsets, Freiman’s theorem
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.4171/JEMS/527
