{"paper":{"title":"Unbounded mean convex domains in Euclidean space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The infimum of mean curvature on any disconnected boundary component of an unbounded mean convex domain in Euclidean space must be zero.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jian Ge","submitted_at":"2026-05-16T04:15:44Z","abstract_excerpt":"In this note, we prove that the infimum of the mean curvature on any disconnected boundary component of an unbounded mean convex domain in $\\mathbb{R}^n$ must be zero."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The infimum of the mean curvature on any disconnected boundary component of an unbounded mean convex domain in R^n must be zero.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The domain is assumed to be mean convex (H ≥ 0) with sufficiently regular boundary to apply the maximum principle or comparison theorems at infinity; this is invoked in the contradiction argument when supposing inf H > 0 on a disconnected component.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves that infimum of mean curvature on any disconnected boundary component of an unbounded mean convex domain in R^n is zero.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The infimum of mean curvature on any disconnected boundary component of an unbounded mean convex domain in Euclidean space must be zero.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"eb35fda8b446351133a945a34091034681f208a62807b0bd5abbe74a16a0caab"},"source":{"id":"2605.16802","kind":"arxiv","version":1},"verdict":{"id":"c49577c5-a07e-4a55-b00a-ae694c3757c4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:36:23.555810Z","strongest_claim":"The infimum of the mean curvature on any disconnected boundary component of an unbounded mean convex domain in R^n must be zero.","one_line_summary":"Proves that infimum of mean curvature on any disconnected boundary component of an unbounded mean convex domain in R^n is zero.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The domain is assumed to be mean convex (H ≥ 0) with sufficiently regular boundary to apply the maximum principle or comparison theorems at infinity; this is invoked in the contradiction argument when supposing inf H > 0 on a disconnected component.","pith_extraction_headline":"The infimum of mean curvature on any disconnected boundary component of an unbounded mean convex domain in Euclidean space must be zero."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16802/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.058542Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:40:53.407225Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.286243Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.422915Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"4cb597701a4170856f187dc92cf97a9edf1668bf8134a68cffc53c892e615753"},"references":{"count":6,"sample":[{"doi":"","year":1992,"title":"Croke and Bruce Kleiner","work_id":"3a9d0f0d-7746-4922-9269-9779ff9c8000","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1980,"title":"The structure of complete stable minimal surfaces in 3 -manifolds of non-negative scalar curvature","work_id":"93ba7a12-81c6-4ff7-a75c-7635d2fe5bb5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Mean Curvature in the Light of Scalar Curvature","work_id":"b99c20a0-65d4-4593-9ebb-e59ba0ee76b3","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1990,"title":"David Hoffman and William H. Meeks, III. The strong halfspace theorem for minimal surfaces. Inventiones Mathematicae , 101(2):373--377, 1990","work_id":"c0617d47-0eb2-429c-aa08-8fa2b839c24c","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1981,"title":"Riemannian manifolds with compact boundary","work_id":"a3c2e4df-9916-41a9-9604-1c739de57938","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":6,"snapshot_sha256":"7b8dce883e23f37b9410fcecee0c4290a0724244b739c2a4c87b19f2fe47f850","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"8b45ba60eaf8a834d8b86633167b34adeea519673ae3fa4733f06cdb851cb14f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}