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The resulting surfaces are complete, have bounded height and are invariant under a discrete group of horizontal translations. In $\\mathbb{S}^2\\times\\mathbb{R}$ (for any $H > 0$) or $\\mathbb{H}^2\\times\\mathbb{R}$ (for $H > 1/2$), a 1-parameter family of unduloid-type surfaces is obtained, some of which are shown to be compact in $\\mathbb{S}^2\\times\\mathbb{R}$. Finally, in the case of $H = 1/2$ in $\\"},"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":"1104.1259","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T07:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"98f729fd0caa0de780ebebec15d3f96ac873eb3876e89afdad0783b99d7a2515","abstract_canon_sha256":"94cb8b611f7f8ba8de791d7355534be14c7651926d0307cde9235b8103a30a94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:27.782859Z","signature_b64":"OcXAnfOWWzYPj8jCxsdvPkj9vmJM7I1KGzUHjWWp+SkRMEIAsqTh2OAPlYfhlLlXEheZfEdaUPa6WjP5cGDuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ba19df6c390b5055955c8d1656e1af0ffc12c66d6515ecd54479b09c6fe554c","last_reissued_at":"2026-05-18T02:31:27.782299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:27.782299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New examples of constant mean curvature surfaces in $\\mathbb{S}^2\\times\\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francisco Torralbo, Jos\\'e M. Manzano","submitted_at":"2011-04-07T07:41:45Z","abstract_excerpt":"We construct non-zero constant mean curvature H surfaces in the product spaces $\\mathbb{S}^2 \\times \\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$ by using suitable conjugate Plateau constructions. The resulting surfaces are complete, have bounded height and are invariant under a discrete group of horizontal translations. In $\\mathbb{S}^2\\times\\mathbb{R}$ (for any $H > 0$) or $\\mathbb{H}^2\\times\\mathbb{R}$ (for $H > 1/2$), a 1-parameter family of unduloid-type surfaces is obtained, some of which are shown to be compact in $\\mathbb{S}^2\\times\\mathbb{R}$. 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