{"paper":{"title":"Small optimal Margulis numbers force upper volume bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Peter B. Shalen","submitted_at":"2010-10-13T19:16:58Z","abstract_excerpt":"If $\\lambda$ is a positive real number strictly less than $\\log3$, there is a positive number $V_\\lambda$ such that every orientable hyperbolic 3-manifold of volume greater than $V_\\lambda$ admits $\\lambda$ as a Margulis number. If $\\lambda<(\\log3)/2$, such a $V_\\lambda$ can be specified explicitly, and is bounded above by $$\\lambda\\bigg(6+\\frac{880}{\\log3-2\\lambda}\\log{1\\over\\log3-2\\lambda}\\bigg),$$ where $\\log$ denotes the natural logarithm. These results imply that for $\\lambda<\\log3$, an orientable hyperbolic 3-manifold that does not have $\\lambda$ as a Margulis number has a rank-2 subgrou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2736","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"}