Conghan Dong

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20192026

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math.DG2026

The Penrose conjecture for initial data sets satisfying a $2$ -convexity condition

Conghan Dong

Let $(M^{3}, g, k)$ be a smooth, connected, asymptotically flat initial data set with connected outermost past apparent horizon $Σ$ . We prove the Penrose conjecture, namely…

math.DG2026

On $3$ -manifolds with small mass and $L^{2}$ -curvature

Conghan Dong, Antoine Song

One of S.T. Yau's problems asks the following: given a $3$ -dimensional asymptotically flat manifold $M$ with non-negative scalar curvature and $L^{2}$ -norm of the curvature tensor at…

math.DG2026

The $σ$ -inverse mean curvature flow and the generalized Penrose conjecture

Conghan Dong

Let $(M^{3}, g, k)$ be a complete asymptotically flat initial data set satisfying the dominant energy condition, and let $m$ denote its ADM mass. The generalized Penrose con…

math.DG2024

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…

math.DG2024

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…

math.DG2019

$W^{1, p}$ -metrics and conformal metrics with $L^{n /2}$ -bounded scalar curvature

Conghan Dong, Yuxiang Li, Ke Xu

A $W^{1, p}$ -metric on an $n$ -dimensional closed Riemannian manifold naturally induces a distance function, provided $p$ is sufficiently close to $n$ . If a sequence of metrics $g_{k}$ …

The Penrose conjecture for initial data sets satisfying a 2-convexity condition

On 3-manifolds with small mass and L2-curvature

The σ-inverse mean curvature flow and the generalized Penrose conjecture

Non-collapsing of Ricci shrinkers with bounded curvature

Stability for the 3D Riemannian Penrose inequality

W1,p-metrics and conformal metrics with Ln/2-bounded scalar curvature

The Penrose conjecture for initial data sets satisfying a $2$ -convexity condition

On $3$ -manifolds with small mass and $L^{2}$ -curvature

The $σ$ -inverse mean curvature flow and the generalized Penrose conjecture

$W^{1, p}$ -metrics and conformal metrics with $L^{n /2}$ -bounded scalar curvature