{"paper":{"title":"Height estimates for $H$-surfaces in the warped product $\\mathbb{M}\\times_f\\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abigail Folha, Carlos Pe\\~nafiel, Walcy Santos","submitted_at":"2018-03-21T19:45:28Z","abstract_excerpt":"In this article, we consider compact surfaces $\\Sigma$ having constant mean curvature $H$ ($H$-surfaces) whose boundary $\\Gamma=\\partial\\Sigma\\subset \\mathbb{M}_0= \\mathbb{M} \\times_f\\{0\\}$ is transversal to the slice $\\mathbb{M}_0$ of the warped product $ \\mathbb{M}\\times_f\\mathbb{R} $, here $ \\mathbb{M} $ denotes a Hadamard surface. We obtain height estimate for a such surface $\\Sigma$ having positive constant mean curvature involving the area of a part of $\\Sigma$ above of $ \\mathbb{M} _0$ and the volume it bounds. Also we give general conditions for the existence of rotationally-invariant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08107","kind":"arxiv","version":1},"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"}