5 papers · 1 filter
Quasi-local Penrose inequalities with electric charge
Po-Ning Chen, Stephen McCormick
The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with non-negative scalar curvature and the area of it…
Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space
Aghil Alaee, Armando J. Cabrera Pacheco, Stephen McCormick
We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown--York quasi-local mass as it possesses positivity and rigidity properties, an…
On the evolution of the spacetime Bartnik mass
Stephen McCormick, Pengzi Miao
It is conjectured that the full (spacetime) Bartnik mass of a surface is realised as the ADM mass of some stationary asymptotically flat manifold with boundary data prescribed…
Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitions
Stephen McCormick
In the context of the Bartnik mass, there are two fundamentally different notions of an extension of some compact Riemannian manifold with boundary. In one case, the extens…
Asymptotically hyperbolic extensions and an analogue of the Bartnik mass
Armando J. Cabrera Pacheco, Carla Cederbaum, Stephen McCormick
The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these mo…