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A Llarull type theorem on complete non-compact manifolds
Abstract
Let 3≤ n≤7, 2≤ k≤ n−1, and m=n−k−1. We prove that a complete, connected, noncompact spin manifold (Mn,g) with scalar curvature RM≥ k(k−1) is isometric to 𝕊k×𝕋mΛ×ℝ if it admits a smooth proper map of nonzero degree to 𝕊k×𝕋m×ℝ whose spherical component is 1-Lipschitz. The flat torus in the conclusion is not necessarily isometric to the target torus.
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BibTeX
@misc{zhu2026llarull,
title = {{A Llarull type theorem on complete non-compact manifolds}},
author = {Guangrui Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20498},
eprint = {2609.20498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20498},
}
RIS
TY - UNPB
TI - A Llarull type theorem on complete non-compact manifolds
AU - Guangrui Zhu
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20498
UR - https://arxiv.org/abs/2609.20498
AB - Let 3≤ n≤7, 2≤ k≤ n−1, and m=n−k−1. We prove that a complete, connected, noncompact spin manifold (M^n,g) with scalar curvature R_M≥ k(k−1) is isometric to 𝕊^k×𝕋^m_Λ×ℝ if it admits a smooth proper map of nonzero degree to 𝕊^k×𝕋^m×ℝ whose spherical component is 1-Lipschitz. The flat torus in the conclusion is not necessarily isometric to the target torus.
ER -