Spacelike hypersurfaces with free boundary in the Minkowski space under the effect of a timelike potential (Q881639)

The author considers a variational principle for space-like hypersurfaces in \((n+1)\)-dimensional Minkowski space. The boundaries of the hypersurfaces are confined to a given space-like hyperplane \(\Pi\). A hypersurface is a solution to the variational problem if its mean curvature is a linear function of the distance to \(\Pi\) and if it makes a constant angle with \(\Pi\) along its boundary. It is proven that any such hypersurface is rotationally symmetric around an axis perpendicular to \(\Pi\).