{"paper":{"title":"Scalar and Mean Curvature Comparison on Compact Cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jie Xu","submitted_at":"2025-07-09T16:35:06Z","abstract_excerpt":"Let $ X $ be a closed, oriented Riemannian manifold. Denote by $ (M = X \\times I, \\partial M = X \\times \\lbrace 0 \\rbrace \\cup X \\times \\lbrace 1 \\rbrace, g) $ a compact cylinder with smooth boundary, $ \\dim M \\geqslant 3 $. In this article, we address the following question: If $ g $ is a Riemannian metric having (i) positive scalar curvature (PSC metric) on $ M $ and nonnegative mean curvature on $ \\partial M $; and (ii) the $ g $-angle between normal vector field $ \\nu_{g} $ along $ \\partial M $ and $ \\partial_{\\xi} \\in \\Gamma(TI) $ being less than $ \\frac{\\pi}{4} $, then there exists a met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07005","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/2507.07005/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"}