Rigidity of spacelike hypersurface with constant curvature and intersection angle condition

Abstract

In the Minkowski space, we consider a compact, spacelike hypersurface with boundary, which can be written as a graph on a spacelike hyperplane. We prove that, if its $k$-th mean curvature is constant, and its boundary is on the hyperplane with constant intersection angles, then the hypersurface must be a part of a hyperboloid, unless it is entirely contained in the hyperplane. The proof is based on an auxiliary function and associated integral equality.