{"paper":{"title":"A quantitative version of the Morse lemma and ideal boundary fixing quasiisometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"LM-Orsay), Vladimir Shchur (DMA","submitted_at":"2011-10-30T18:19:03Z","abstract_excerpt":"The article is devoted to a proof of the optimal upper-bound for Morse Lemma, its \"anti\"-version and their applications. Roughly speaking, Morse Lemma states that in a hyperbolic metric space, a $\\lambda$-quasi-geodesic $\\gamma$ sits in a $\\lambda^2$-neighborhood of every geodesic $\\sigma$ with same endpoints. Anti-Morse Lemma states that $\\sigma$ sits in a $\\log\\lambda$-neighborhood of $\\gamma$. Applications include the displacement of points under quasi-isometries fixing the ideal boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6630","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"}