{"paper":{"title":"Quantum ergodic restriction theorems, II: manifolds without boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"J. A. Toth, S. Zelditch","submitted_at":"2011-04-23T05:12:19Z","abstract_excerpt":"We prove that if $(M, g)$ is a compact Riemannian manifold with ergodic geodesic flow, and if $H \\subset M$ is a smooth hypersurface satisfying a generic asymmetry condition with respect to the geodesic flow, then restrictions $\\phi_j |_H$ of an orthonormal basis $\\{\\phi_j\\}$ of $\\Delta$-eigenfunctions of $(M, g)$ to $H$ are quantum ergodic on $H$. The condition on $H$ is satisfied by geodesic circles, closed horocycles and generic closed geodesics on a hyperbolic surface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4531","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"}