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In particular, the total curvature of $\\Gamma_5<4\\pi$ and thus any minimal surface $\\Sigma \\subset \\mathbb{R}^n$ bounded by $\\Gamma_5$ is embedded. Let $\\Gamma_5$ be a piecewise geodesic Jordan curve with $5$ vertices in $\\mathbb{H}^n$. Then any minimal surface $\\Sigma \\subset \\mathbb{H}^n$ bounded by $\\Gamma_5$ is embedded. If $\\Gamma_5$ is in a geodes"},"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":"1011.4140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-18T06:27:04Z","cross_cats_sorted":[],"title_canon_sha256":"ca5262c7a72c39fb0a989392936f6c31b707821184442fa94f7ea38dffd72d81","abstract_canon_sha256":"b878368bfb773f86b68d8b26134265402ac47bcf2aef86e87faa19bb813c21a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:46.542522Z","signature_b64":"IbuJ5t9Mi4zQx9uENLsE2jobXffkkdEc8KvaIYELQzfKilwMsd612fDweUS2AlVVmJ59FKUKWoH61TO5rCXRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49b3b9e6fc91ae8c424b60b65d8d2e8060f85e7530a2a20904614f3c7d4b2a23","last_reissued_at":"2026-05-18T04:35:46.541993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:46.541993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embeddedness of proper minimal submanifolds in homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Sung-Hong Min","submitted_at":"2010-11-18T06:27:04Z","abstract_excerpt":"We prove the three embeddedness results as follows. $({\\rm i})$ Let $\\Gamma_{2m+1}$ be a piecewise geodesic Jordan curve with $2m+1$ vertices in $\\mathbb{R}^n$, where $m$ is an integer $\\geq2$. 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