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Open AccessImpact of a Mathematics Bridging Course on the Motivation and Learning Skills of University Students
The transition from secondary to tertiary education is an exciting and yet challenging event in the educational biography of students. During this transition, students often meet with unexpected challenges, wh...
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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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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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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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Open AccessEffective versions of the positive mass theorem
The study of stable minimal surfaces in Riemannian 3-manifolds (M, g) with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when (M, g) is asymptotically flat an...
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Large outlying stable constant mean curvature spheres in initial data sets
We give examples of asymptotically flat three-manifolds \((M,g)\) ( M ...
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Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
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Deformation of scalar curvature and volume
The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified probl...
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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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Extension of a theorem of Shi and Tam
In this note, we prove the following generalization of a theorem of Shi and Tam (J Differ Geom 62:79–125, 2002): Let (Ω, g) be an n-dimensional (n ≥ 3) compact Riemannian manifold, spin when n > 7, with non-negat...
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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.
