3 papers
math.DG2026
Foliation of area-minimizing hypersurfaces in asymptotically flat manifolds of higher dimension
Shihang He, Yuguang Shi, Haobin Yu
We prove the existence of foliations by area-minimizing hypersurfaces in asymptotically flat (AF) manifolds with arbitrary dimension and arbitrary ends. Also we provide behaviors o…
math.DG2026
Singularity removal rigidity theorems for minimal hypersurfaces in manifolds with nonnegative scalar curvature
Shihang He, Yuguang Shi, Haobin Yu
We prove two "Singularity removal rigidity theorems" for minimal hypersurfaces with isolated singularities in manifolds of nonnegative scalar curvature (Theorems \ref{thm: rigidity…
math.DG2025
Positive mass theorems on singular spaces and some applications
Shihang He, Yuguang Shi, Haobin Yu
Building upon dimension reduction techniques in the study of positive scalar curvature (PSC) geometry, we prove an effective version of the positive mass theorem (PMT) for asymptot…