Constant mean curvature foliations of flat space-times

Let V be a maximal globally hyperbolic flat n + 1-dimensional space-time with compact Cauchy surface of hyperbolic type. We prove that V is globally foliated by constant mean curvature hypersurfaces M-tau, with mean curvature tau taking all values in (-infinity, 0). For n greater than or equal to 3, define the rescaled volume of M-tau by H = \tau\(n)Vol (M, g), where g is the induced metric. Then H greater than or equal to n(n)Vol (M, g(0)) where g(0) is the hyperbolic metric on M with sectional curvature -1. Equality holds if and only if (M, g) is isometric to (M, g(0)).