12 citations · 18 across the 8 of their papers we have counts for
8 papers
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…
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…
Isoperimetry for asymptotically flat 3-manifolds with positive ADM mass
Haobin Yu
Let be an asymptotically flat 3-manifold with positive ADM mass. In this paper, we show that each leaf of the canonical foliation is the unique isoperimetric surface for…
On the Rigidity of Riemannian-Penrose Inequality for Asymptotically Flat 3-manifolds with Corners
Yuguang Shi, Wenlong Wang, Haobin Yu
In this paper we prove a rigidity result for the equality case of the Penrose inequality on -dimensional asymptotically flat manifolds with nonnegative scalar curvature and corn…
Isoperimetry, scalar curvature, and mass in asymptotically flat Riemannian -manifolds
Otis Chodosh, Michael Eichmair, Yuguang Shi +1
Let be an asymptotically flat Riemannian -manifold with non-negative scalar curvature and positive mass. We show that each leaf of the canonical foliation through stabl…
Evolving hypersurfaces by their mean curvature in the background manifold evolving by Ricci flow
Weimin Sheng, Haobin Yu
We consider the problem of deforming a one-parameter family of hypersurfaces immersed into closed Riemannian manifolds with positive curvature operator. The hypersurface in this fa…