| dc.contributor.author | Figalli, Alessio | |
| dc.contributor.author | Jerison, David S | |
| dc.date.accessioned | 2018-05-23T13:46:01Z | |
| dc.date.available | 2018-05-23T13:46:01Z | |
| dc.date.issued | 2015-05 | |
| dc.identifier.issn | 1435-9855 | |
| dc.identifier.uri | http://hdl.handle.net/1721.1/115583 | |
| dc.description.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 | en_US |
| dc.publisher | European Mathematical Publishing House | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.4171/JEMS/527 | en_US |
| dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
| dc.source | arXiv | en_US |
| dc.title | Quantitative stability for sumsets in R[superscript n] | en_US |
| dc.type | Article | en_US |
| dc.identifier.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. | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
| dc.contributor.mitauthor | Jerison, David S | |
| dc.relation.journal | Journal of the European Mathematical Society | en_US |
| dc.eprint.version | Author's final manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
| dc.date.updated | 2018-05-22T17:10:08Z | |
| dspace.orderedauthors | Figalli, Alessio; Jerison, David | en_US |
| dspace.embargo.terms | N | en_US |
| dc.identifier.orcid | https://orcid.org/0000-0002-9357-7524 | |
| mit.license | OPEN_ACCESS_POLICY | en_US |
