{"paper":{"title":"Weighted centro-affine Poincar\\'e inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Mohammad N. Ivaki, Yingxiang Hu","submitted_at":"2026-06-03T11:55:04Z","abstract_excerpt":"We obtain weighted centro-affine Bochner formulas on spherical caps associated with smooth strictly convex hypersurfaces. As a consequence, we prove weighted Poincar\\'e inequalities on caps and on intersections of caps for a class of weights depending on the position vector $X$ of the hypersurface. In the unconditional case, we obtain a centro-affine Poincar\\'e inequality with weight $|X|^2$, which is used to prove a Brunn--Minkowski inequality for the $(n+2)$-nd dual quermassintegral.\n  We also establish an $L_0$-Brunn--Minkowski inequality for the $q$-th dual quermassintegral for $q\\in(0,n)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04774","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04774/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}