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Moreover, in case $M$ is $\\h^n,\\r^n$ or $\\s_+^n$ and each of its boundary components is embedded then $\\Sigma$ is rotationally invariant. When $M$ has dimension 2 and Gaussian curvature bounded from below by a positive constant $\\kappa,$ we prove there is no stable CMC with free boundary connecting the boundar"},"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":"1802.06848","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-19T21:01:32Z","cross_cats_sorted":[],"title_canon_sha256":"dd483666cc0b582fa56ed4c9cb7a92c7c8ec03bba7999627210a67f0c20e0fec","abstract_canon_sha256":"5c01d0c12d890c69b53f63c93346514c1d062ed6a8a5d1b5b18d93369d395bf2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:34.131354Z","signature_b64":"enq3NEEe/leErtHgQ10SCPB1jxmVEcO7JRL6EKbD6rGbDVma9cKyRMcF15DNhlYD6v88jznF0Tl82Ylhr3+JBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72ea9b96cc668857ed43c93363e90b43efe35c3bba5e326fada954c6624c60e7","last_reissued_at":"2026-05-17T23:52:34.130924Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:34.130924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable constant mean curvature surfaces with free boundary in slabs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rabah Souam","submitted_at":"2018-02-19T21:01:32Z","abstract_excerpt":"We study stable constant mean curvature (CMC) hypersurfaces $\\Sigma$ in slabs in a product space $M\\times\\r,$ where $M$ is an orientable Riemannian manifold. 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