Monotonicidade da área para superfícies tipo-espaço com curvatura média constante

Abstract

We study compact spacelike surfaces with constant mean curvature in the threedimensional Lorentz-Minkowski space (...). When the boundary of the surface is a planar curve, we obtain an estimate for the height of the surface measured from the plane (...) that contains the boundary. We show that this height cannot extend more that (...) above (...), where A and H denote respectively, the area of the surface that lies over (...) and the mean curvature of the surface. Moreover, this estimative is attained if and only if the surface is a planar domain (with H = 0) or a hyperbolic cap (with H 0).