几何分析讨论班

报告题目：Singularity removal rigidity theorem for minimal hypersurfaces with isolated singularities in manifolds of nonnegative scalar curvature

报 告 人：于浩斌 教授（杭州师范大学）

时  间：2026年6月3日（星期三），上午9:30-10:30

地  点：海纳苑2幢205

摘  要：In this talk we will present the “Singularity removal rigidity theorem” for minimal hypersurfaces with isolated singularities in manifolds of nonnegative scalar curvature. In particular, we observe a new phenomenon that the extremal scalar curvature condition forces smoothness, which reveals a kind of positive effect of minimal hypersurface singularities in scalar curvature geometry. As an application, we obtain a direct proof of the positive mass theorem (PMT) for asymptotically flat 8-manifolds with arbitrary ends without using N. Smale's generic regularity theorem. A key ingredient is a new spectral version of PMT for AF manifolds with arbitrary ends, whose proof relies on PMT for asymptotically locally flat (ALF) manifolds with S^1-symmetry. This talk is based on joint work with Shihang He and Prof. Yuguang Shi.