13 citations · 37 across the 7 of their papers we have counts for
5 papers · 1 filter
Noncompact Fill-Ins of Bartnik Data
Dan A. Lee, Martin Lesourd, Ryan Unger
We generalize Y. Shi and L.-F.\ Tam's \cite{ShiTam} nonnegativity result for the Brown-York mass, by considering nonnegative scalar curvature (NNSC) fill-ins that need only be comp…
Density and positive mass theorems for incomplete manifolds
Dan A. Lee, Martin Lesourd, Ryan Unger
For manifolds with a distinguished asymptotically flat end, we prove a density theorem which produces harmonic asymptotics on the distinguished end, while allowing for points of in…
Density and positive mass theorems for initial data sets with boundary
Dan A. Lee, Martin Lesourd, Ryan Unger
We prove a harmonic asymptotics density theorem for asymptotically flat initial data sets with compact boundary that satisfy the dominant energy condition. We use this to settle th…
The Positive Mass Theorem with Arbitrary Ends
Martin Lesourd, Ryan Unger, Shing-Tung Yau
We prove a Riemannian positive mass theorem for manifolds with a single asymptotically flat end, but otherwise arbitrary other ends, which can be incomplete and contain negative sc…
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…