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

Abstract

In this paper we develop some integral formulas for compact spacelike surfaces (necessarily with non-empty boundary) with constant mean curvature in the Lorentz-Minkowski three-space. As an application of this, when the boundary 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 also obtain a uniqueness result for compact spacelike surfaces with constant mean curvature whose boundary projects onto a planar Jordan curve contained in a spacelike plane.