中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
几何拓扑研讨班
Speaker: 尤江城（中国科学技术大学）
Inviter: 王晋民
Language: 中文
Title: Green Functions and Rigidity under Nonnegative Scalar Curvature
Time & Venue：2026年9月10日（星期四） 9:30-10:30 思源楼S615
Abstract: We discuss two rigidity problems for complete 3-manifolds with nonnegative scalar curvature. First, we prove Gromov's endpoint C⁰ rigidity conjecture: a complete metric on ℝ³ satisfying |g−g_Euc|=o(|x|⁻¹) and having nonnegative scalar curvature must be Euclidean. Second, we prove that every contractible 3-manifold admitting a complete metric of nonnegative scalar curvature is diffeomorphic to ℝ³, and that the interior of a handlebody admitting such a metric must have genus at most one. Although these results concern different forms of rigidity, their proofs share a potential-theoretic viewpoint, using Green functions and geometric identities for their level sets to translate scalar-curvature information into global rigidity. This is joint work with Heng Zhang（张衡）.
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