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Here, $K'$ ranges over all symmetric convex bodies contained in $K$.\\\\ P2) What is the maximal possible volume of the Blaschke-body of a convex body of volume 1?\\\\ Our main result states that (P1) and (P2) admit precisely the same solutions. This complements a result from [{\\rm K. B\\\"or\\\"oczky, I. B\\'ar\\'any, E. Makai Jr. and J. Pach}, Maximal volume enclosed by plates and proof of the chessboard conjecture], Di"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.4955","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-20T04:43:56Z","cross_cats_sorted":[],"title_canon_sha256":"914006b1420c50d789aab3aa55c534bbd4a13d1754bd96c6ac3b21e98798f652","abstract_canon_sha256":"fa1f9467545cde94937fc1e02cfde7b6c1171daa283da693168ba679270b5d6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:01.382682Z","signature_b64":"MLDkzixQqBpJBDJAGASbfzRGcGcTfBFVQZ3tbuQV7DoA/f9WP/FLXCLMtjooBNFTeLOyd3JSIPaDIZ7tDtWKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a29f0f2a753a26cdbf000422b8239760993850ee99467cfe94b6bb9d9677c37","last_reissued_at":"2026-05-18T02:33:01.382349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:01.382349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the equivalence between two problems of asymmetry on convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christos Saroglou","submitted_at":"2013-11-20T04:43:56Z","abstract_excerpt":"The simplex was conjectured to be the extremal convex body for the two following \"problems of asymmetry\":\\\\ P1) What is the minimal possible value of the quantity $\\max_{K'} |K'|/|K|$? Here, $K'$ ranges over all symmetric convex bodies contained in $K$.\\\\ P2) What is the maximal possible volume of the Blaschke-body of a convex body of volume 1?\\\\ Our main result states that (P1) and (P2) admit precisely the same solutions. This complements a result from [{\\rm K. B\\\"or\\\"oczky, I. B\\'ar\\'any, E. Makai Jr. and J. 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