{"paper":{"title":"Concerning the Wave equation on Asymptotically Euclidean Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengbo Wang, Christopher D. Sogge","submitted_at":"2008-12-30T22:18:58Z","abstract_excerpt":"We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on $(\\R^d, \\mathfrak{g})$, $d \\geq 3$, when metric $\\mathfrak{g}$ is non-trapping and approaches the Euclidean metric like $ x ^{- \\rho}$ with $\\rho>0$. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for $\\rho> 1$ and $d=3$. Also, we establish the Strauss conjecture when the metric is radial with $\\rho>0$ for $d= 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0022","kind":"arxiv","version":4},"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"}