{"paper":{"title":"Steady Ricci solitons with horizontally $\\epsilon$-pinched Ricci curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaohua Zhu, Yuxing Deng","submitted_at":"2016-01-09T13:42:32Z","abstract_excerpt":"In this paper, we prove that any $\\kappa$-noncollapsed gradient steady Ricci soliton with nonnegative curvature operator and horizontally $\\epsilon$-pinched Ricci curvature must be rotationally symmetric. As an application, we show that any $\\kappa$-noncollapsed gradient steady Ricci soliton $(M^n, g,f)$ with nonnegative curvature operator must be rotationally symmetric if it admits a unique equilibrium point and its scalar curvature $R(x)$ satisfies $\\lim_{r(x)\\rightarrow\\infty}R(x)f(x)=C_0\\sup_{x\\in M}R(x)$ with $C_0>\\frac{n-2}{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02111","kind":"arxiv","version":3},"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"}