{"paper":{"title":"Beyond almost Fuchsian space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Ben Lowe, Zheng Huang","submitted_at":"2021-04-22T18:56:32Z","abstract_excerpt":"An almost Fuchsian manifold is a hyperbolic 3-manifold of the type $S\\times \\mathbb{R}$ which admits a closed minimal surface (homeomorphic to $S$) with the maximum principal curvature $\\lambda_0 <1$, while a weakly almost Fuchsian manifold is of the same type but it admits a closed minimal surface with $\\lambda_0 <= 1$. We first prove that any weakly almost Fuchsian manifold is geometrically finite, and we construct a Canary-Storm type compactification for the weakly almost Fuchsian space. We use this to prove uniform upper bounds on the volume of the convex core and Hausdorff dimension for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.11284","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.11284/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}