Area monotonicity for spacelike surfaces with constant mean curvature

We study compact spacelike surfaces with constant mean curvature in the three-dimensional Lorentz-Minkowski space L-3. When the boundary of the surface is a planar curve, we obtain an estimate for the height of the surface measured from the plane Pi that contains the boundary. We show that this height cannot extend more that A\H\/(2pi) above Pi, where A and H denote, respectively, the area of the surface that lies over Pi and the mean curvature of the surface. Moreover, this estimate is attained if and only if the surface is a planar domain (with H = 0) or a hyperbolic cap (with H not equal 0). (C) 2004 Elsevier B.V. All rights reserved.