6 Result(s)
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Article
Open AccessDoubling of Asymptotically Flat Half-spaces and the Riemannian Penrose Inequality
Building on previous works of Bray, of Miao, and of Almaraz, Barbosa, and de Lima, we develop a doubling procedure for asymptotically flat half-spaces (M, g) with horizon boundary
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Article
Open AccessThe Willmore Center of Mass of Initial Data Sets
We refine the Lyapunov–Schmidt analysis from our recent paper (Eichmair and Koerber in Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds. ar**v preprint ar**v:2...
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Article
Open AccessInitial Data Rigidity Results
We prove several rigidity results related to the spacetime positive mass theorem. A key step is to show that certain marginally outer trapped surfaces are weakly outermost. As a special case, our results inclu...
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Article
Open AccessCharacterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data
Let (M, g) be a complete Riemannian 3-manifold asymptotic to Schwarzschild-anti-deSitter and with scalar curvature \({R \geq - 6}\) ...
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Article
The Jang Equation Reduction of the Spacetime Positive Energy Theorem in Dimensions Less Than Eight
We extend the Jang equation proof of the positive energy theorem due to Schoen and Yau (Commun Math Phys 79(2):231–260, 1981) from dimension n = 3 to dimensions 3 ≤ n < 8. This requires us to address several te...
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Article
Existence, Regularity, and Properties of Generalized Apparent Horizons
We prove a conjecture of Tom Ilmanen and Hubert Bray on the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.
