{"paper":{"title":"Asymptotically Moebius maps and rigidity for the hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alessio Savini","submitted_at":"2019-06-25T14:30:28Z","abstract_excerpt":"Let $S$ be a rank-one symmetric space of non-compact type and let $X$ be a $\\text{CAT}(-1)$ space. A well-known result by Bourdon states that if a topological embedding $\\varphi: \\partial_\\infty S \\rightarrow \\partial_\\infty X$ respects cross ratios, that means $\\text{cr}_S( \\xi_0,\\eta_0,\\xi_1,\\eta_1)=\\text{cr}_X( \\varphi(\\xi_0),\\varphi(\\eta_0),\\varphi(\\xi_1),\\varphi(\\eta_1))$ for every $\\xi_0,\\eta_0,\\xi_1,\\eta_1 \\in \\partial_\\infty S$, then $\\varphi$ is induced by an isometric embedding of $S$ into $X$.\n  We generalize this result when $S=\\mathbb{H}^2$ is the real hyperbolic plane as it follo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10563","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"}