6 papers
The Penrose conjecture for initial data sets satisfying a -convexity condition
Conghan Dong
Let be a smooth, connected, asymptotically flat initial data set with connected outermost past apparent horizon . We prove the Penrose conjecture, namely…
On -manifolds with small mass and -curvature
Conghan Dong, Antoine Song
One of S.T. Yau's problems asks the following: given a -dimensional asymptotically flat manifold with non-negative scalar curvature and -norm of the curvature tensor at…
The -inverse mean curvature flow and the generalized Penrose conjecture
Conghan Dong
Let be a complete asymptotically flat initial data set satisfying the dominant energy condition, and let denote its ADM mass. The generalized Penrose con…
Stability for the 3D Riemannian Penrose inequality
Conghan Dong
We show that the Schwarzschild 3-manifold is stable for the 3-dimensional Riemannian Penrose inequality in the pointed measured Gromov-Hausdorff topology, modulo negligible domains…
Non-collapsing of Ricci shrinkers with bounded curvature
Conghan Dong, Yu Li
We establish a uniform entropy bound for simply connected Ricci shrinkers with a finite second homotopy group and a uniform curvature bound. Additionally, we extend the non-collaps…
Stability of Euclidean 3-space for the positive mass theorem
Conghan Dong, Antoine Song
We show that the Euclidean 3-space is stable for the Positive Mass Theorem in the following sense. Let be a sequence of complete asymptotically flat -…