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math.DG2020★ 6 cited
Positive Scalar Curvature on Noncompact Manifolds and the Liouville Theorem
Martin Lesourd, Ryan Unger, Shing-Tung Yau
Using minimal hypersurfaces, we obtain topological obstructions to admitting complete metrics with positive scalar curvature on a given class of non-compact n-manifolds with n less…
math.DG2020
Stable Surfaces and Free Boundary Marginally Outer Trapped Surfaces
Aghil Alaee, Martin Lesourd, Shing-Tung Yau
We explore various notions of stability for surfaces embedded and immersed in spacetimes and initial data sets. The interest in such surfaces lies in their potential to go beyond t…
math.AP2020
Construction of Cauchy data for the dynamical formation of apparent horizons and the Penrose Inequality
Nikolaos Athanasiou, Martin Lesourd
Based on scale critical initial data, we construct smooth asymptotically flat Cauchy initial data for the Einstein vacuum system that does not contain Marginally Outer Trapped Surf…