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New examples of static spacetimes admitting a unique standard decomposition
(SpringerLink, 2019)
In this paper we introduce a new general approach for the study of spacetimes admitting a standard static splitting. This approach allows us to give an alternative proof for the uniqueness of splitting in the spatially ...
Calabi-Bernstein type problems in Lorentzian Geometry
(Springer, 2017)
The study of maximal hypersurfaces in Lorentzian manifolds is an interesting mathematical problem, which connects di_erential geometry, nonlinear partial di_erential equations and certain problems in mathematical relativity. ...
Stable Minimal Surfaces in Riemannian Warped Products
(Springer, 2017)
We obtain several stability results forminimal two-sided surfaces immersed in a wide class of 3-dimensional Riemannian warped products, which includes the class of Riemannian products. As a consequence, some Bernstein-type ...
An analytical approach to the external force-free motion of pendulums on surfaces of constant curvature
(Elsevier, 2018)
The dynamics of external force free motion of pendulums on surfaces of constant Gaussian curvature is addressed when the pivot moves along a geodesic obtaining the Lagrangian of the system. As an application it is possible ...
Spacelike hypersurfaces with functionally bounded mean curvature in Lorentzian warped products and generalized Calabi-Bernstein type problems
(Cambridge University Press, 2019)
We study spacelike hypersurfaces with functionally bounded mean curvature in Lorentzian warped products M = I × f F , where F is a (non-compact) complete Riemannian mani- fold whose universal covering is parabolic. In ...
Compact maximal hypersurfaces in globally hyperbolic spacetimes
(IOP Publishing, 2018)
Several uniqueness results on compact maximal hypersurfaces in a wide class of globally hyperbolic spacetimes are provided. They are obtained from the study of a distinguished function on the maximal hypersurface and under ...
Stability of maximal hypersurfaces in spacetimes: new general conditions and application to relevant spacetimes
(Springer, 2017)
We obtain new simple sufficient conditions to ensure the stability and strong stability of maximal hypersurfaces (without boundary) immersed in an arbitrary spacetime. Several applications to maximal hypersurfaces in a ...
Galilean Generalized Robertson-Walker spacetimes: a new family of Galilean geometrical models
(American Institute of Physics, 2018)
We introduce a new family of Galilean spacetimes, the Galilean generalized Robertson-Walker spacetimes. This new family is relevant in the context of a generalized Newton-Cartan theory. We study its geometrical structure ...