On the existence of spacelike constant mean curvature surfaces spanning two circular contours in Minkowski space

Consider the Plateau problem for spacelike surfaces with constant mean curvature in three-dimensional Lorentz–Minkowski space L3L3 and spanning two circular axially symmetric contours in parallel planes. In this paper, we prove that rotational symmetric surfaces are the only solutions. We also give a result on uniqueness of spacelike surfaces of revolution with constant mean curvature as solutions of the exterior Dirichlet problem under a certain hypothesis at infinity.