{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JYU2GHHMOFVMSMQSMP3IHBQXTA","short_pith_number":"pith:JYU2GHHM","schema_version":"1.0","canonical_sha256":"4e29a31cec716ac9321263f68386179810f848184e9a5c702ce7852b12a6bd72","source":{"kind":"arxiv","id":"1501.07357","version":2},"attestation_state":"computed","paper":{"title":"Isoperimetric domains in homogeneous three-manifolds and the isoperimetric constant of the Heisenberg group $\\mathsf{H}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Malchiodi, Jih-Hsin Cheng, Paul Yang","submitted_at":"2015-01-29T07:18:34Z","abstract_excerpt":"In this paper we prove that isoperimetric sets in three-dimensional homogeneous spaces diffeomorphic to $\\mathbb{R}^3$ are topological balls. We also prove that in three-dimensional homogeneous spheres isopermetric sets are either two-spheres or symmetric genus-one tori. We then apply our first result to the three-dimensional Heisenberg group $\\mathsf{H}^1$, characterizing the isoperimetric sets and constants for a family of Riemannian adapted metrics. Using $\\Gamma$-convergence of the perimeter functionals, we also settle an isoperimetric conjecture in $\\mathsf{H}^1$ posed by P.Pansu."},"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":"1501.07357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-29T07:18:34Z","cross_cats_sorted":[],"title_canon_sha256":"7bd2a877b66bdbd17c7a97ccb8bc3707512f1344ab5125f8b3902793992ae336","abstract_canon_sha256":"006bc69314e674c8f5f03c204aed2c20aa8b95b8404008cdde96aafd7fca18bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:00.499168Z","signature_b64":"OiMzZ3oy8rSTU/nRwUWUKC9yJNcSQ+5Q4WCPUEtJOGXGN/y0XhqIHuF5RyEujubMAAxiXCZhivXXDNcTPoBQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e29a31cec716ac9321263f68386179810f848184e9a5c702ce7852b12a6bd72","last_reissued_at":"2026-05-18T02:27:00.498796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:00.498796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isoperimetric domains in homogeneous three-manifolds and the isoperimetric constant of the Heisenberg group $\\mathsf{H}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Malchiodi, Jih-Hsin Cheng, Paul Yang","submitted_at":"2015-01-29T07:18:34Z","abstract_excerpt":"In this paper we prove that isoperimetric sets in three-dimensional homogeneous spaces diffeomorphic to $\\mathbb{R}^3$ are topological balls. We also prove that in three-dimensional homogeneous spheres isopermetric sets are either two-spheres or symmetric genus-one tori. We then apply our first result to the three-dimensional Heisenberg group $\\mathsf{H}^1$, characterizing the isoperimetric sets and constants for a family of Riemannian adapted metrics. Using $\\Gamma$-convergence of the perimeter functionals, we also settle an isoperimetric conjecture in $\\mathsf{H}^1$ posed by P.Pansu."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07357","kind":"arxiv","version":2},"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":"1501.07357","created_at":"2026-05-18T02:27:00.498856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.07357v2","created_at":"2026-05-18T02:27:00.498856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07357","created_at":"2026-05-18T02:27:00.498856+00:00"},{"alias_kind":"pith_short_12","alias_value":"JYU2GHHMOFVM","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JYU2GHHMOFVMSMQS","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JYU2GHHM","created_at":"2026-05-18T12:29:27.538025+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/JYU2GHHMOFVMSMQSMP3IHBQXTA","json":"https://pith.science/pith/JYU2GHHMOFVMSMQSMP3IHBQXTA.json","graph_json":"https://pith.science/api/pith-number/JYU2GHHMOFVMSMQSMP3IHBQXTA/graph.json","events_json":"https://pith.science/api/pith-number/JYU2GHHMOFVMSMQSMP3IHBQXTA/events.json","paper":"https://pith.science/paper/JYU2GHHM"},"agent_actions":{"view_html":"https://pith.science/pith/JYU2GHHMOFVMSMQSMP3IHBQXTA","download_json":"https://pith.science/pith/JYU2GHHMOFVMSMQSMP3IHBQXTA.json","view_paper":"https://pith.science/paper/JYU2GHHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.07357&json=true","fetch_graph":"https://pith.science/api/pith-number/JYU2GHHMOFVMSMQSMP3IHBQXTA/graph.json","fetch_events":"https://pith.science/api/pith-number/JYU2GHHMOFVMSMQSMP3IHBQXTA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JYU2GHHMOFVMSMQSMP3IHBQXTA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JYU2GHHMOFVMSMQSMP3IHBQXTA/action/storage_attestation","attest_author":"https://pith.science/pith/JYU2GHHMOFVMSMQSMP3IHBQXTA/action/author_attestation","sign_citation":"https://pith.science/pith/JYU2GHHMOFVMSMQSMP3IHBQXTA/action/citation_signature","submit_replication":"https://pith.science/pith/JYU2GHHMOFVMSMQSMP3IHBQXTA/action/replication_record"}},"created_at":"2026-05-18T02:27:00.498856+00:00","updated_at":"2026-05-18T02:27:00.498856+00:00"}