10 papers
Capillary prisms, Coxeter gluing, and the -systole of 3-manifolds with positive scalar curvature
Shihang He, Chao Li
We study the -systole of positive scalar curvature -manifolds via a local-to-global approach. The tessellated local building blocks are capillary prisms : Riemannian cyl…
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…
Finite generation of Noether-Lefschetz divisors and the slope of the moduli space of cubic fourfolds
Ignacio Barros, Shi He, Paul Kiefer
We study divisors on moduli spaces of cubic fourfolds with simple singularities and of quasi-polarized K3 surfaces of degree . For the moduli space of cubic fourfolds, we intro…
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…
Foliation of area minimizing hypersurfaces in asymptotically flat manifolds and Schoen's conjecture
Shihang He, Yuguang Shi, Haobin Yu
In this paper, we demonstrate that any asymptotically flat manifold with can be foliated by a family of area-minimizing hypersurfaces, each of which is a…
Relative aspherical conjecture and higher codimensional obstruction to positive scalar curvature
Shihang He
Motivated by the solution of the aspherical conjecture up to dimension 5 [CL20][Gro20], we want to study a relative version of the aspherical conjecture. We present a natural condi…
A note on rational homology vanishing theorem for hypersurfaces in aspherical manifolds
Shihang He, Jintian Zhu
In this note, we generalize Gromov's reduction \cite{Gro20} from the aspherical conjecture to the generalized filling radius conjecture to the smooth -homology vanishing…
Twisted stability and positive scalar curvature obstruction on fiber bundles
Shihang He
We establish several non-existence results of positive scalar curvature (PSC) on fiber bundles. We show that under an incompressible condition of the fiber, for a Cartan-Hada…