{"paper":{"title":"Near Equality in the Brunn-Minkowski Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael Christ","submitted_at":"2012-07-20T21:18:34Z","abstract_excerpt":"A pair of subsets of Euclidean space which nearly achieves equality in the Brunn-Minkowski inequality must nearly coincide with a pair of homothetic convex sets. The two-dimensional case was treated in a previous paper in this series by an argument which does not seem to generalize to higher dimensions. Here the result is extended to arbitrary dimensions. An induction on the dimension, a symmetrization argument, and a description of near solutions of an additive functional equation are used to establish sufficient regularity to set up a compactness argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5062","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"}