{"paper":{"title":"Interior curvature estimates and the asymptotic plateau problem in hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bo Guan, Joel Spruck, Ling Xiao","submitted_at":"2012-09-20T18:37:52Z","abstract_excerpt":"We show that for a very general class of curvature functions defined in the positive cone, the problem of finding a complete strictly locally convex hypersurface in $H^n+1$ satisfying $f(\\kappa)=\\sigma\\in(0, 1)$ with a prescribed asymptotic boundary $\\Gamma$ at infinity has at least one smooth solution with uniformly bounded hyperbolic principal curvatures. Moreover if $\\Gamma$ is (Euclidean) starshaped, the solution is unique and also (Euclidean) starshaped while if $\\Gamma$ is mean convex the solution is unique. We also show via a strong duality theorem that analogous results hold in De Sitt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4601","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"}