{"paper":{"title":"Lorentzian Einstein metrics with prescribed conformal infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.DG","math.MP"],"primary_cat":"math.AP","authors_text":"Alberto Enciso, Niky Kamran","submitted_at":"2014-12-14T16:23:00Z","abstract_excerpt":"We prove a local well-posedness theorem for the (n+1)-dimensional Einstein equations in Lorentzian signature, with initial data $(\\tilde g, K)$ whose asymptotic geometry at infinity is similar to that anti-de Sitter (AdS) space, and compatible boundary data $\\hat g$ prescribed at the time-like conformal boundary of space-time. More precisely, we consider an n-dimensional asymptotically hyperbolic Riemannian manifold $(M,\\tilde g)$ such that the conformally rescaled metric $x^2 \\tilde g$ (with $x$ a boundary defining function) extends to the closure $\\bar M$ of $M$ as a metric of class $C^{n-1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4376","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"}