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We show that the least value of the isoperimetric ratio is attained for an $(m+1)$-dimensional flat half-disk of $\\mathbb{R}^{n+1}_+$. This extends prior work of Choe, Ghomi, and Ritor\\'{e} in codimension one and proves a conjecture of Choe in the case of relative area minimizers."},"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":"1710.04821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-13T06:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"6a94cab14684598f8accabb9c41b1caf60e211ddb724f582be35305cc31ae13f","abstract_canon_sha256":"2bac4efdac82a3836fc557f0e728639f97582f12425475d326b065b9e50c9102"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:56.617784Z","signature_b64":"e5FRqMjMfp8lZSmgnS1UbqAHcV0oMBpmnR3rNlug8gMcU653Y1bkOw+QRy3cJANFlNZ0d4WrbhiIongNYgJ5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"308bc823cb034147266662f5283782b612cdf3b9684130459a982d8907d51d41","last_reissued_at":"2026-05-18T00:32:56.617076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:56.617076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher codimension relative isoperimetric inequality outside a convex set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Brian Krummel","submitted_at":"2017-10-13T06:29:17Z","abstract_excerpt":"We consider an isoperimetric inequality for $(m+1)$-dimensional area minimizing submanifolds of arbitrary codimension which lie outside a convex set $\\mathcal{K} \\subset \\mathbb{R}^{n+1}$ and are bounded by a submanifold of $\\mathbb{R}^{n+1} \\setminus \\mathcal{K}$ and the convex set $\\mathcal{K}$. We show that the least value of the isoperimetric ratio is attained for an $(m+1)$-dimensional flat half-disk of $\\mathbb{R}^{n+1}_+$. This extends prior work of Choe, Ghomi, and Ritor\\'{e} in codimension one and proves a conjecture of Choe in the case of relative area minimizers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04821","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.04821","created_at":"2026-05-18T00:32:56.617181+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.04821v1","created_at":"2026-05-18T00:32:56.617181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04821","created_at":"2026-05-18T00:32:56.617181+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCF4QI6LANAU","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCF4QI6LANAUOJTG","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCF4QI6L","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY","json":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY.json","graph_json":"https://pith.science/api/pith-number/GCF4QI6LANAUOJTGML2SQN4CWY/graph.json","events_json":"https://pith.science/api/pith-number/GCF4QI6LANAUOJTGML2SQN4CWY/events.json","paper":"https://pith.science/paper/GCF4QI6L"},"agent_actions":{"view_html":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY","download_json":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY.json","view_paper":"https://pith.science/paper/GCF4QI6L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.04821&json=true","fetch_graph":"https://pith.science/api/pith-number/GCF4QI6LANAUOJTGML2SQN4CWY/graph.json","fetch_events":"https://pith.science/api/pith-number/GCF4QI6LANAUOJTGML2SQN4CWY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY/action/storage_attestation","attest_author":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY/action/author_attestation","sign_citation":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY/action/citation_signature","submit_replication":"https://pith.science/pith/GCF4QI6LANAUOJTGML2SQN4CWY/action/replication_record"}},"created_at":"2026-05-18T00:32:56.617181+00:00","updated_at":"2026-05-18T00:32:56.617181+00:00"}