{"paper":{"title":"On the characterization of minimal surfaces with finite total curvature in $\\mathbb H^2\\times\\mathbb R$ and $\\widetilde{\\rm PSL}_2(\\mathbb{R},\\tau)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ana Menezes, Laurent Hauswirth, Magdalena Rodr\\'iguez","submitted_at":"2016-04-24T21:16:35Z","abstract_excerpt":"It is known that a complete immersed minimal surface with finite total curvature in $\\mathbb H^2\\times\\mathbb R$ is proper, has finite topology and each one of its ends is asymptotic to a geodesic polygon at infinity (Hauswirth and Rosenberg, 2006; Hauswirth, Nelli, Sa Earp and Toubiana, 2015). In this paper we prove that these three properties characterize complete immersed minimal surfaces with finite total curvature in $\\mathbb H^2\\times\\mathbb R$. As corollaries of this theorem we obtain characterizations for minimal Scherk-type graphs and horizontal catenoids in $\\mathbb H^2\\times\\mathbb "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07083","kind":"arxiv","version":2},"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"}