{"paper":{"title":"Four-dimensional shrinkers with nonnegative Ricci curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Guoqiang Wu, Jia-Yong Wu","submitted_at":"2025-05-05T02:20:12Z","abstract_excerpt":"In this paper, we investigate classifications of $4$-dimensional simply connected complete noncompact nonflat shrinkers satisfying $Ric+\\mathrm{Hess}\\,f=\\tfrac 12g$ with nonnegative Ricci curvature. One one hand, we show that if the sectional curvature $K\\le 1/4$ or the sum of smallest two eigenvalues of Ricci curvature has a suitable lower bound, then the shrinker is isometric to $\\mathbb{R}\\times\\mathbb{S}^3$. We also show that if the scalar curvature $R\\le 3$ and the shrinker is asymptotic to $\\mathbb{R}\\times\\mathbb{S}^3$, then the Euler characteristic $\\chi(M)\\geq 0$ and equality holds if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02315","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/2505.02315/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"}