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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 ...
Relativistic particles with torsion in three-dimensional non-vacuum spacetimes
(American Institute of Physics, 2021)
In this paper, we analyze trajectories of spacelike curves that are critical points of a Lagrangian depending on its total torsion. We focus on two important families of spacetimes, generalized Robertson–Walker and standard ...
A Moser–Bernstein problem for Riemannian warped products
(Springer, 2020)
In this work we deal with an elliptic non-linear problem, which arises naturally from Riemannian geometry. This problem has classically been studied in the the Euclidean n-dimensional space and it is known as the Moser–Bernstein ...
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 ...