{"paper":{"title":"Lens rigidity for manifolds with hyperbolic trapped set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS"],"primary_cat":"math.AP","authors_text":"Colin Guillarmou","submitted_at":"2014-12-04T18:42:21Z","abstract_excerpt":"For a Riemannian manifold $(M,g)$ with strictly convex boundary $\\partial M$, the lens data consists in the set of lengths of geodesics $\\gamma$ with endpoints on $\\partial M$, together with their endpoints $(x_-,x_+)\\in \\partial M\\times \\partial M$ and tangent exit vectors $(v_-,v_+)\\in T_{x_-} M\\times T_{x_+} M$. We show deformation lens rigidity for a large class of manifolds which includes all manifolds with negative curvature and strictly convex boundary, possibly with non-trivial topology and trapped geodesics. For the same class of manifolds in dimension $2$, we prove that the set of en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1760","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"}