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Giladi","submitted_at":"2019-08-21T14:44:15Z","abstract_excerpt":"Given a convex body K in R^n and p in R, we introduce and study the extremal inner and outer affine surface areas\n  IS_p(K) = sup_{K'\\subseteq K} (as_p(K') ) and os_p(K)=inf_{K'\\supseteq K} (as_p(K') ), where as_p(K') denotes the L_p-affine surface area of K', and the supremum is taken over all convex subsets of K and the infimum over all convex compact subsets containing K.\n  The convex body that realizes IS_1(K) in dimension 2 was determined by Barany. He also showed that this body is the limit shape of lattice polytopes in K. In higher dimensions no results are known about the extremal bodi"},"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":"1908.07897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-21T14:44:15Z","cross_cats_sorted":[],"title_canon_sha256":"0706aa07b297d56eb60dcfcdc5c44f293112325dbc2d687a8caeae2174846924","abstract_canon_sha256":"3c9f0fde6743b924c1123714cbfef1f371c2abe7e91cfed19397a0cb4c07eb1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:43:19.752713Z","signature_b64":"J7lmTbvOy1S0jcMrDESCz+Dus3aIeyy/K1CeG+YR2kiq2sIBlqDBybw6rgtCzKEWbbxjofFiSVKiWq+xi46RCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54c90ba4e00d8785bc221d0d13cadbef7d292aa0b5fcd79fa8ff2233ce5ec380","last_reissued_at":"2026-07-05T00:43:19.752237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:43:19.752237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constrained convex bodies with extremal affine surface areas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C. 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