Area monotonicity for spacelike surfaces with constant mean curvature

Abstract

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 Π that contains the boundary. We show that this height cannot extend more that A| H|/(2 π) above Π, where A and H denote, respectively, the area of the surface that lies over Π 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≠0).