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This note shows that replacing Young's inequality by H\\\"older's inequality at this stage yields a structurally simpler argument, a strictly smaller constant, and a natural extension to the constant-mean-curvature (CMC) setting. Starting from the standard preparatory gradient estimate, we derive explicit constants $C_Y(n,q)$ and $C_H(n,q)$ for the Young and H\\\"older closure rout"},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.17466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-17T14:07:53Z","cross_cats_sorted":[],"title_canon_sha256":"8fca408087766c0eb68cfa0c86c4164fa3207fb8beb7fecf49620e08b7f45060","abstract_canon_sha256":"ffcad4c0950d26a4989b107c6d689736e0b4edcbece94497552f313ba8350e32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:40.402099Z","signature_b64":"Sx6hueCJwYgfCChOM8B7PGlflit6LAdsDTShsi14E4ZKKO5B5CZ6ALanqc2MUBmtKNd9jP39Kjs/MeSzPLoIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"825798407b3461cd9fa4fe8763e0f4c25637b7037d515859484b3ac0e58ed13d","last_reissued_at":"2026-05-20T00:04:40.401069Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:40.401069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Terminal H\\\"older Closure in Curvature Estimates and its Application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Replacing Young's inequality with Hölder's simplifies curvature estimates and extends to CMC hypersurfaces.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Anji Tang","submitted_at":"2026-05-17T14:07:53Z","abstract_excerpt":"The Schoen--Simon--Yau (SSY) curvature estimate reduces the Bernstein problem for complete stable minimal graphs in $\\mathbb{R}^{n+1}$ to an integral estimate whose final step traditionally relies on Young's inequality. 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