{"paper":{"title":"A quantitative version of a theorem by Jungreis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG"],"primary_cat":"math.GT","authors_text":"Cristina Pagliantini, Michelle Bucher, Roberto Frigerio","submitted_at":"2015-03-12T18:28:13Z","abstract_excerpt":"A fundamental result by Gromov and Thurston asserts that, if M is a closed hyperbolic n-manifold, then the simplicial volume |M| of M is equal to vol(M)/v_n, where v_n is a constant depending only on the dimension of M. The same result also holds for complete finite-volume hyperbolic manifolds without boundary, while Jungreis proved that the ratio vol(M)/|M| is strictly smaller than v_n if M is compact with non-empty geodesic boundary. We prove here a quantitative version of Jungreis' result for n>3, which bounds from below the ratio |M|/vol(M) in terms of the ratio between the volume of the b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03837","kind":"arxiv","version":1},"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"}