{"paper":{"title":"Fill-Ins of Tori with Scalar Curvature Bounded from Below","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yipeng Wang","submitted_at":"2024-11-22T02:02:11Z","abstract_excerpt":"Let $\\gamma$ be a Riemannian metric on $\\Sigma = S^1 \\times T^{n-2}$, where $3 \\leq n \\leq 7$. Consider $\\Omega = B^2 \\times T^{n-2}$ with boundary $\\partial \\Omega = \\Sigma$, and let $g$ be a Riemannian metric on $\\Omega$ such that the scalar curvature $R_g \\geq -n(n - 1)$ and $g|_{\\partial \\Omega} = \\gamma$. Assuming the mean curvature of $\\partial \\Omega$ with respect to the outward normal is positive, we establish that the total mean curvature of $\\partial \\Omega$ is bounded from above by a constant depending only on $n$ and $\\gamma$. Furthermore, we compute the sharp constant for this est"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14667","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14667/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"}