{"paper":{"title":"Inverse problems for semilinear wave equations on Lorentzian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gunther Uhlmann, Matti Lassas, Yiran Wang","submitted_at":"2016-06-20T19:25:49Z","abstract_excerpt":"We consider inverse problems in space-time $(M, g)$, a $4$-dimensional Lorentzian manifold. For semilinear wave equations $\\square_g u + H(x, u) = f$, where $\\square_g$ denotes the usual Laplace-Beltrami operator, we prove that the source-to-solution map $L: f \\rightarrow u|_V$, where $V$ is a neighborhood of a time-like geodesic $\\mu$, determines the topological, differentiable structure and the conformal class of the metric of the space-time in the maximal set where waves can propagate from $\\mu$ and return back. Moreover, on a given space-time $(M, g)$, the source-to-solution map determines"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06261","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"}