Spacelike Hypersurfaces with Free Boundary in the Minkowski Space under the Effect of a Timelike Potential

Abstract

In this paper we consider a variational problem for spacelike hypersurfaces in the (n + 1)-dimensional Lorentz-Minkowski space \(\mathbb{L}^{n+1}\), whose critical points are hypersurfaces supported in a spacelike hyperplane Π determined by two facts: the mean curvature is a linear function of the distance to Π and the hypersurface makes a constant angle with Π along its boundary. We prove that the hypersurface is rotational symmetric with respect to a straight-line orthogonal to Π and that each (non-empty) intersection with a parallel hyperplane to Π is a round (n − 1)-sphere. A similar result is proved for hypersurfaces trapped between two parallel hyperplanes.