{"ID":23603867,"CreatedAt":"2026-09-18T06:00:06.305330393Z","UpdatedAt":"2026-09-18T06:00:06.305330393Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20498","arxiv_id":"2609.20498","title":"A Llarull type theorem on complete non-compact manifolds","abstract":"Let $3\\leq n\\leq7$, $2\\leq k\\leq n-1$, and $m=n-k-1$. We prove that a complete, connected, noncompact spin manifold $(M^n,g)$ with scalar curvature $R_M\\geq k(k-1)$ is isometric to $\\mathbb{S}^k\\times\\mathbb{T}^m_Λ\\times\\mathbb{R}$ if it admits a smooth proper map of nonzero degree to $\\mathbb{S}^k\\times\\mathbb{T}^m\\times\\mathbb{R}$ whose spherical component is 1-Lipschitz. The flat torus in the conclusion is not necessarily isometric to the target torus.","short_abstract":"Let $3\\leq n\\leq7$, $2\\leq k\\leq n-1$, and $m=n-k-1$. We prove that a complete, connected, noncompact spin manifold $(M^n,g)$ with scalar curvature $R_M\\geq k(k-1)$ is isometric to $\\mathbb{S}^k\\times\\mathbb{T}^m_Λ\\times\\mathbb{R}$ if it admits a smooth proper map of nonzero degree to $\\mathbb{S}^k\\times\\mathbb{T}^m\\ti...","url_abs":"https://arxiv.org/abs/2609.20498","url_pdf":"https://arxiv.org/pdf/2609.20498v1","authors":"[\"Guangrui Zhu\"]","published":"2026-09-17T14:45:37Z","proceeding":"math.DG","tasks":"[\"math.DG\"]","methods":"[]","has_code":false}