4 papers
A proof for the Riemannian positive mass theorem up to dimension 19
Yuchen Bi, Tianze Hao, Shihang He +2
In this paper, we prove the Riemannian positive mass theorem up to dimension , building on a combination of torical symmetrization and the singularity blow-up technique develop…
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…
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…
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…