{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JQIIBK3MSTA4BIBKXVCJSUZABY","short_pith_number":"pith:JQIIBK3M","schema_version":"1.0","canonical_sha256":"4c1080ab6c94c1c0a02abd449953200e3f37285ee43725ed0078cfcbab2a72e5","source":{"kind":"arxiv","id":"1701.00290","version":4},"attestation_state":"computed","paper":{"title":"Heinz mean curvature estimates in warped product spaces $M\\times_{e^{\\psi}}N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Isabel M.C. Salavessa","submitted_at":"2017-01-01T21:40:18Z","abstract_excerpt":"If a graph submanifold $(x,f(x))$ of a Riemannian warped product space $(M^m\\times_{e^{\\psi}}N^n,\\tilde{g}=g+e^{2\\psi}h)$ is immersed with parallel mean curvature $H$, then we obtain a Heinz type estimation of the mean curvature. Namely, on each compact domain $D$ of $M$, $m\\|H\\|\\leq \\frac{A_{\\psi}(\\partial D)}{V_{\\psi}(D)}$ holds, where $A_{\\psi}(\\partial D)$ and $V_{\\psi}(D)$ are the ${\\psi}$-weighted area and volume, respectively. In particular, $H=0$ if $(M,g)$ has zero weighted Cheeger constant, a concept recently introduced by D.\\ Impera et al.\\ (\\cite{[Im]}). This generalizes the known "},"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":"1701.00290","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-01T21:40:18Z","cross_cats_sorted":[],"title_canon_sha256":"2673e3ba0cba59eeb55b0fc3801573e03dd8aa653b5d86866d02b5c2ee03da72","abstract_canon_sha256":"c9b3055ce4da916498dfa8e193b650f0a89bdfa51b4fbae0cc3d6a42bd23cdae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:35.350994Z","signature_b64":"HsZzyZUVypwCyE1Ef3DAUJujFANKnqLlZiTLwPYL1CuFlKMm7YB2/B+HeQOqVtA9NoFgAblbVbuVspuN82mJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c1080ab6c94c1c0a02abd449953200e3f37285ee43725ed0078cfcbab2a72e5","last_reissued_at":"2026-05-18T00:21:35.350252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:35.350252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heinz mean curvature estimates in warped product spaces $M\\times_{e^{\\psi}}N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Isabel M.C. Salavessa","submitted_at":"2017-01-01T21:40:18Z","abstract_excerpt":"If a graph submanifold $(x,f(x))$ of a Riemannian warped product space $(M^m\\times_{e^{\\psi}}N^n,\\tilde{g}=g+e^{2\\psi}h)$ is immersed with parallel mean curvature $H$, then we obtain a Heinz type estimation of the mean curvature. Namely, on each compact domain $D$ of $M$, $m\\|H\\|\\leq \\frac{A_{\\psi}(\\partial D)}{V_{\\psi}(D)}$ holds, where $A_{\\psi}(\\partial D)$ and $V_{\\psi}(D)$ are the ${\\psi}$-weighted area and volume, respectively. In particular, $H=0$ if $(M,g)$ has zero weighted Cheeger constant, a concept recently introduced by D.\\ Impera et al.\\ (\\cite{[Im]}). This generalizes the known "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00290","kind":"arxiv","version":4},"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":"1701.00290","created_at":"2026-05-18T00:21:35.350381+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.00290v4","created_at":"2026-05-18T00:21:35.350381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00290","created_at":"2026-05-18T00:21:35.350381+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQIIBK3MSTA4","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQIIBK3MSTA4BIBK","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQIIBK3M","created_at":"2026-05-18T12:31:24.725408+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/JQIIBK3MSTA4BIBKXVCJSUZABY","json":"https://pith.science/pith/JQIIBK3MSTA4BIBKXVCJSUZABY.json","graph_json":"https://pith.science/api/pith-number/JQIIBK3MSTA4BIBKXVCJSUZABY/graph.json","events_json":"https://pith.science/api/pith-number/JQIIBK3MSTA4BIBKXVCJSUZABY/events.json","paper":"https://pith.science/paper/JQIIBK3M"},"agent_actions":{"view_html":"https://pith.science/pith/JQIIBK3MSTA4BIBKXVCJSUZABY","download_json":"https://pith.science/pith/JQIIBK3MSTA4BIBKXVCJSUZABY.json","view_paper":"https://pith.science/paper/JQIIBK3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.00290&json=true","fetch_graph":"https://pith.science/api/pith-number/JQIIBK3MSTA4BIBKXVCJSUZABY/graph.json","fetch_events":"https://pith.science/api/pith-number/JQIIBK3MSTA4BIBKXVCJSUZABY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQIIBK3MSTA4BIBKXVCJSUZABY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQIIBK3MSTA4BIBKXVCJSUZABY/action/storage_attestation","attest_author":"https://pith.science/pith/JQIIBK3MSTA4BIBKXVCJSUZABY/action/author_attestation","sign_citation":"https://pith.science/pith/JQIIBK3MSTA4BIBKXVCJSUZABY/action/citation_signature","submit_replication":"https://pith.science/pith/JQIIBK3MSTA4BIBKXVCJSUZABY/action/replication_record"}},"created_at":"2026-05-18T00:21:35.350381+00:00","updated_at":"2026-05-18T00:21:35.350381+00:00"}