{"paper":{"title":"A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.MG","authors_text":"Galyna V. Livshyts","submitted_at":"2021-06-30T20:45:49Z","abstract_excerpt":"We show that for any log-concave measure $\\mu$ on $\\mathbb{R}^n$, any pair of symmetric convex sets $K$ and $L$, and any $\\lambda\\in [0,1],$ $$\\mu((1-\\lambda) K+\\lambda L)^{c_n}\\geq (1-\\lambda) \\mu(K)^{c_n}+\\lambda\\mu(L)^{c_n},$$ where $c_n\\geq n^{-4-o(1)}.$ This constitutes progress towards the dimensional Brunn-Minkowski conjecture (see Gardner, Zvavitch \\cite{GZ}, Colesanti, L, Marsiglietti \\cite{CLM}). Moreover, our bound improves for various special classes of log-concave measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.00095","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"}