Quantitative stability for sumsets in
Alessio Figalli
ETH Zürich, SwitzerlandDavid Jerison
Massachusetts Institute of Technology, Cambridge, USA
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Abstract
Given a measurable set of positive measure, it is not difficult to show that if and only if is equal to its convex hull minus a set of measure zero. We investigate the stability of this statement: If is small, is close to its convex hull? Our main result is an explicit control, in arbitrary dimension, on the measure of the difference between and its convex hull in terms of .
Cite this article
Alessio Figalli, David Jerison, Quantitative stability for sumsets in . J. Eur. Math. Soc. 17 (2015), no. 5, pp. 1079–1106
DOI 10.4171/JEMS/527