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This corresponds with the estimates available for Euclidean space (except for the endpoint $(q,r) = (2, \\frac{2n}{n-2})$ whe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0408273","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2004-08-20T05:21:35Z","cross_cats_sorted":[],"title_canon_sha256":"f01c75eb2c5d71d56c350115da66878d798bef4670e1d07c45e0a2f1862b236c","abstract_canon_sha256":"d8ca2c0f8f56ca9344c006042cd8aaaee0bacf62eb42b9b2d7d58b3f8c96163c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.073857Z","signature_b64":"Cyt3BoO5ZFFOdNZEztiybPthiExJkLH27Z3svK81HZ0go8YCz1QffNCL8Uyw9Bbr13YllBPBq0p9FxHr0oSmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a9b760a109a7235cd75c5685ec754314fbfae61372f85416d819e8603966d96","last_reissued_at":"2026-05-18T01:05:26.073276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.073276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Strichartz estimates on non-trapping asymptotically conic manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Jared Wunsch, Terence Tao","submitted_at":"2004-08-20T05:21:35Z","abstract_excerpt":"We obtain the Strichartz inequalities $$ \\| u \\|_{L^q_t L^r_x([0,1] \\times M)} \\leq C \\| u(0) \\|_{L^2(M)}$$ for any smooth $n$-dimensional Riemannian manifold $M$ which is asymptotically conic at infinity (with either short-range or long-range metric perturbation) and non-trapping, where $u$ is a solution to the Schr\\\"odinger equation $iu_t + {1/2} \\Delta_M u = 0$, and $2 < q, r \\leq \\infty$ are admissible Strichartz exponents ($\\frac{2}{q} + \\frac{n}{r} = \\frac{n}{2}$). 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