{"paper":{"title":"The convexification effect of Minkowski summation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Arnaud Marsiglietti, Artem Zvavitch, Matthieu Fradelizi, Mokshay Madiman","submitted_at":"2017-04-18T18:21:20Z","abstract_excerpt":"Let us define for a compact set $A \\subset \\mathbb{R}^n$ the sequence $$ A(k) = \\left\\{\\frac{a_1+\\cdots +a_k}{k}: a_1, \\ldots, a_k\\in A\\right\\}=\\frac{1}{k}\\Big(\\underset{k\\ {\\rm times}}{\\underbrace{A + \\cdots + A}}\\Big). $$ It was independently proved by Shapley, Folkman and Starr (1969) and by Emerson and Greenleaf (1969) that $A(k)$ approaches the convex hull of $A$ in the Hausdorff distance induced by the Euclidean norm as $k$ goes to $\\infty$. We explore in this survey how exactly $A(k)$ approaches the convex hull of $A$, and more generally, how a Minkowski sum of possibly different compac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05486","kind":"arxiv","version":3},"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"}