Solutions to mean curvature equations in weighted standard static spacetimes

Abstract

In this article, we study the solutions for the mean curvature equation in a weighted standard static spacetime, \(\mathbb{P}_f^n\times_\rho\mathbb{R}_1\), having a warping function \(\rho\) whose weight function f does not depend on the parameter \(t\in\mathbb{R}\). We establish a f-parabolicity criterion to study the rigidity of spacelike hypersurfaces immersed in \(\mathbb{P}_f^n\times_\rho\mathbb{R}_1\) and, in particular, of entire Killing graphs constructed over the Riemannian base \(\mathbb{P}^n\). Also we give applications to weighted standard static spacetimes of the type \(\mathbb{G}^n\times_\rho\mathbb{R}_1\), where \(\mathbb G^n\) is the Gaussian space. For more information see https://ejde.math.txstate.edu/Volumes/2020/83/abstr.html