Convexity of the solutions to the constant mean curvature spacelike surface equation in the Lorentz-Minkowski space

We prove that a spacelike graph of constant mean curvature H≠0 in the 3-dimensional Lorentz-Minkowski space over a bounded domain with pseudo-elliptic boundary is strictly convex. By a pseudo-elliptic curve we mean a closed and planar curve which intersects any branch of any hyperbola at most at five points. We also provide an example that shows that we cannot remove the assumption on the boundary being a pseudo-elliptic curve.