{"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 $\\mathbb{S}^2\\times\\mathbb{R}$. Finally, in the case of $H = 1/2$ in $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1259","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}