{"paper":{"title":"Resonance free regions for nontrapping manifolds with cusps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Kiril Datchev","submitted_at":"2009-10-28T03:12:23Z","abstract_excerpt":"This paper has been withdrawn because of a mistake in Lemma 7.4. For a corrected version of the main theorem, as well as various further developments and applications, see arXiv:1210.7736. For nonpositively curved perturbations of parabolic cylinders we establish the existence of a logarithmically large resonance free region. We use an escape function construction in a compact part of the manifold and near infinity we use the method of complex scaling. To the author's knowledge this is the first proof of a large resonance free region for manifolds with cusps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5283","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"}