Solutions to mean curvature equations in weighted standard static spacetimes




de Lima, Henrique F.
Ramalho, Andre F. A.
Velasquez, Marco Antonio

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Texas State University, Department of Mathematics


In this article, we study the solutions for the mean curvature equation in a weighted standard static spacetime, ℙnƒ x ρℝ1, having a warping function ρ whose weight function ƒ does not depend on the parameter t ∈ ℝ. We establish a ƒ-parabolicity criterion to study the rigidity of spacelike hypersurfaces immersed in ℙnƒ x ρℝ1 and, in particular, of entire Killing graphs constructed over the Riemannian base ℙn. Also we give applications to weighted standard static spacetimes of the type Gn x ρℝ1, where Gn is the Gaussian space.



Standard static spacetimes with density, Gaussian space, F-parabolic spacelike hypersurface, Entire Killing graphs, Mean curvature equation


de Lima, H. F., Ramalho, A. F. A., & Velásquez, M. A. L. (2020). Solutions to mean curvature equations in weighted standard static spacetimes. Electronic Journal of Differential Equations, 2020(83), pp. 1-19.


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