7 papers · 1 filter
A Minkowski inequality for Horowitz-Myers geon
Aghil Alaee, Pei-Ken Hung
We prove a sharp inequality for toroidal hypersurfaces in three and four dimensional Horowitz-Myers geon. This extend previous results on Minkowski inequality in the static spaceti…
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…
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…
Geometric Inequalities for Quasi-Local Masses
Aghil Alaee, Marcus Khuri, Shing-Tung Yau
In this paper lower bounds are obtained for quasi-local masses in terms of charge, angular momentum, and horizon area. In particular we treat three quasi-local masses based on a Ha…
Positive mass theorem for initial data sets with corners along a hypersurface
Aghil Alaee, Shing-Tung Yau
We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptot…
Asymptotically flat extensions with charge
Aghil Alaee, Armando J. Cabrera Pacheco, Carla Cederbaum
The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically fla…