Solutions to mean curvature equations in weighted standard static spacetimes
de Lima, Henrique F.
Ramalho, Andre F. A.
Velasquez, Marco Antonio
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. <i>Electronic Journal of Differential Equations, 2020</i>(83), pp. 1-19.
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