{"paper":{"title":"On the asymptotic Plateau problem for CMC hypersurfaces in hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jaime Ripoll, Miriam Telichevesky","submitted_at":"2015-03-27T14:06:31Z","abstract_excerpt":"Let $\\mathbb{R}_{+}^{n+1}$ \\ be the half-space model of the hyperbolic space $\\mathbb{H}^{n+1}.$ It is proved that if $\\Gamma\\subset\\left\\{ x_{n+1}=0\\right\\} \\subset\\partial_{\\infty}\\mathbb{H}^{n+1}$ is a bounded $C^{0}$ Euclidean graph over $\\left\\{ x_{1}=0,\\text{ }x_{n+1}=0\\right\\} $ then, given $\\left\\vert H\\right\\vert <1,$ there is a complete, properly embedded, CMC $H$ hypersurface $\\Sigma$ of $\\mathbb{H}^{n+1}$ such that $\\partial_{\\infty }S=\\Gamma\\cup\\left\\{ x_{n+1}=+\\infty\\right\\} .$ This result can be seen as a limit case of the existence theorem proved by B. Guan and J. Spruck in \\ci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08083","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"}