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For each $\\omega \\in S^{d-1}$, we have that the $(d-1)$-volume of the intersection of $K$ and an arbitrary hyperplane, with normal $\\omega$, attains its maximum if the hyperplane contains $0$. An analogous theorem, for $1$-dimensional sections and $1$-volumes, has been proved long ago by Hammer (\\cite{H}). In this paper we deal with the ($(d-2)$-dimensional) surface area, or"},"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":"1507.01467","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-06T14:00:53Z","cross_cats_sorted":[],"title_canon_sha256":"4ec1bc56fa51f5f3173d72325b2c9988cc7f3f1262dcc5577a45ba43962c4ef4","abstract_canon_sha256":"4a5c67b58bf11553d19d53fadee011150f58d0635d990d369ea8fc2512636be7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:16.852799Z","signature_b64":"e3vknc+hpdB97g6q0ixew91b7kdWWE/o+VEJRseqZDFdHAmVfsABGznuxeJDh7OICCmnU3RPEz69vS7eCpApDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26aabe6af2a2e210e175acefea09bf7b9f7d7ee59390dca11b25e9a0ccf26cdf","last_reissued_at":"2026-05-18T01:37:16.852207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:16.852207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Centrally symmetric convex bodies and sections having maximal quermassintegrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"E. 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