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.

Stable maximal hypersurfaces in Lorentzian spacetimes / Colombo, Giulio; Pelegrín, José A. S.; Rigoli, Marco. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 179:(2019), pp. 354-382. [10.1016/j.na.2018.09.009]

Stable maximal hypersurfaces in Lorentzian spacetimes

COLOMBO, GIULIO;
2019

Abstract

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.
2019
Stable maximal hypersurfaces in Lorentzian spacetimes / Colombo, Giulio; Pelegrín, José A. S.; Rigoli, Marco. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 179:(2019), pp. 354-382. [10.1016/j.na.2018.09.009]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/938697
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