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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 ...
Complete spacelike hypersurfaces on symmetric spacetimes
(IOP Publishing, 2020)
A Lorentz manifold (M, g) is said to be a conformally stationary spacetime if it is endowed with a globally defined conformal timelike vector field K, whereas it is a pp-wave when there is a globally defined parallel ...
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 ...
Compact Minimal Submanifolds in a Large Class of Riemannian Manifolds
(Springer, 2023)
Through a new technique, we provide uniqueness, rigidity and non-existence results for compact minimal submanifolds of arbitrary dimension in a large class of Riemannian manifolds, which include between others, Riemannian ...
On complete trapped submanifolds in globally hyperbolic spacetimes
(IOP Publishing, 2023)
The aim of this manuscript is to obtain rigidity and non-existence results for parabolic spacelike submanifolds with causal mean curvature vector field in orthogonally splitted spacetimes, and in particular, in globally ...
On the connectedness of a random closed set of a Euclidean space
(Elsevier, 2022)
Our aim is to obtain a suitable characterization of certain topological properties of a random closed set through its capacity
functional. The main technique mixes two different fields: on the one hand, the abstract ...