{"paper":{"title":"Curvature estimates for hypersurfaces of constant curvature in hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Bin Wang","submitted_at":"2022-05-27T03:07:50Z","abstract_excerpt":"In this note, we prove that for every $0<\\sigma<1$, there exists a smooth complete hypersurface $\\Sigma$ in $\\mathbb{H}^{n+1}$ with prescribed asymptotic boundary $\\partial \\Sigma=\\Gamma$ at infinity, whose principal curvatures $\\kappa=(\\kappa_1,\\ldots,\\kappa_n)$ lie in a general cone $K$ and satisfy $f(\\kappa)=\\sigma$ at each point of $\\Sigma$. Previously, the problem has been studied by Guan-Spruck in [J. Eur. Math. Soc. (JEMS) 12 (2010), no. 3, 797-817], and they proved the existence result for $\\sigma \\in (\\sigma_0,1)$, where $\\sigma_0>0$. A major ingredient of our proof is a refined curva"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.13739","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.13739/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}