{"paper":{"title":"On the asymptotic Plateau's problem for CMC hypersurfaces on rank 1 symmetric spaces of noncompact type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jaime Ripoll, Jean-Baptiste Casteras","submitted_at":"2014-03-05T15:29:35Z","abstract_excerpt":"Let $M$ be a Hadamard manifold with curvature bounded above by a negative constant $-\\alpha$, satisfying the \"strict convexity condition\", and assume that $M$ admits a \"helicoidal\" one-parameter subgroup $G$ of isometries of $M$. Then, given a compact topological $G-$shaped hypersurface $\\Gamma$ in the asymptotic boundary of $M,$ and $|H|<\\sqrt{\\alpha}$, we prove the existence of a complete properly embedded hypersurface whose mean curvature is equal to $H$ and whose asymptotic boundary is $\\Gamma$. We are able, this way, to extend a previous theorem of B.Guan and J.Spruck on the hyperbolic sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1160","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"}