We study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions, for instance the Timelike Convergence Condition (TCC). We characterize stability when the target space has constant sectional curvature as well as give sufficient conditions on the geometry of the ambient spacetime (e.g., the validity of TCC) to ensure stability. Some rigidity results and height estimates are also proven in GRW spacetimes. In the last part of the paper we consider k-stability of spacelike hypersurfaces, a concept related to mean curvatures of higher orders.
|Titolo:||Stable maximal hypersurfaces in Lorentzian spacetimes|
|Parole Chiave:||Generalized Robertson–Walker spacetime; k-stability; Spacetime of constant sectional curvature; Stable maximal hypersurface; Analysis; Applied Mathematics|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||2019|
|Digital Object Identifier (DOI):||10.1016/j.na.2018.09.009|
|Appare nelle tipologie:||01 - Articolo su periodico|