{"paper":{"title":"Quantitative stability for the Brunn-Minkowski inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Alessio Figalli, David Jerison","submitted_at":"2014-12-24T02:37:47Z","abstract_excerpt":"We prove a quantitative stability result for the Brunn-Minkowski inequality: if $|A|=|B|=1$, $t \\in [\\tau,1-\\tau]$ with $\\tau>0$, and $|tA+(1-t)B|^{1/n}\\leq 1+\\delta$ for some small $\\delta$, then, up to a translation, both $A$ and $B$ are quantitatively close (in terms of $\\delta$) to a convex set $K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06513","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}