Stable maximal hypersurfaces in Lorentzian spacetimes
| Autor: | Marco Rigoli, Giulio Colombo, José A. S. Pelegrín |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Differential Geometry
Spacetime Applied Mathematics 010102 general mathematics Mathematical analysis Rigidity (psychology) Curvature Space (mathematics) 01 natural sciences Stability (probability) 010101 applied mathematics General Relativity and Quantum Cosmology Differential Geometry (math.DG) Primary: 53C24 53C42 35J20 Secondary: 35P15 53C50 53C80 83C99 FOS: Mathematics Mathematics::Differential Geometry Sectional curvature 0101 mathematics Variety (universal algebra) Constant (mathematics) Analysis Mathematics |
| Zdroj: | Nonlinear Analysis. 179:354-382 |
| ISSN: | 0362-546X |
| DOI: | 10.1016/j.na.2018.09.009 |
| Popis: | 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. Comment: 30 pages. This is a pre-print of an article published in Nonlinear Analysis. The final authenticated version is available online at: https://doi.org/10.1016/j.na.2018.09.009 |
| Databáze: | OpenAIRE |
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