{"paper":{"title":"Remarks on planar Blaschke-Santal\\'o inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"E. Makai Jr, K. J. B\\\"or\\\"oczky","submitted_at":"2014-11-14T09:43:04Z","abstract_excerpt":"We prove the Blaschke-Santal\\'o inequality restricted to $n$-gons: the extremal polygons are the affine regular $n$-gons. If either the John or the L\\\"owner ellipse of a planar $o$-symmetric convex body $K$ is the unit circle about $o$, then a sharpening of the Blaschke-Santal\\'o inequality holds: even the aritmetic mean $\\left( V(K) + V( K^*) \\right) /2 $ is at least $\\pi $. We give stability variants of the Blaschke-Santal\\'o inequality for the plane. If for some $n \\ge 3$ the planar convex body $K$ is $n$-fold rotationally symmetric about $o$, then we give the exact maximum of $V(K^*)$, as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3842","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"}