Compact spacelike surfaces with constant mean curvature in the Lorentz-Minkowski 3-space

In this paper we develop some integral formulas for compact spacelike surfa ces (necessarily with non-empty boundary) with constant mean curvature in t he Lorentz-Minkowski three-space. As an application of this, when the bound ary is a circle, we prove that the only such surfaces are the planar discs and the hyperbolic caps. By means of an appropriate maximum principle, we a lso obtain a uniqueness result for compact spacelike surfaces with constant mean curvature whose boundary projects onto a planar Jordan curve containe d in a spacelike plane.