{"paper":{"title":"Scattering theory of the Hodge-Laplacian under a conformal perturbation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.DG","authors_text":"Batu G\\\"uneysu, Francesco Bei, J\\\"orn M\\\"uller","submitted_at":"2014-07-02T16:14:52Z","abstract_excerpt":"Let $g$ and $\\tilde{g}$ be Riemannian metrics on a noncompact manifold $M$, which are conformally equivalent. We show that under a very mild \\emph{first order} control on the conformal factor, the wave operators corresponding to the Hodge-Laplacians $\\Delta_g$ and $\\Delta_{\\tilde{g}}$ acting on differential forms exist and are complete. We apply this result to Riemannian manifolds with a bounded geometry and more specifically, to warped product Riemannian manifolds with a bounded geometry. Finally, we combine our results with some explicit calculations by Antoci to determine the absolutely con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0630","kind":"arxiv","version":3},"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"}