Constant Mean
نویسنده
چکیده
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 Mτ , with mean curvature τ taking all values in (−∞, 0). For n ≥ 3, define the rescaled volume of Mτ by H = |τ | Vol(M, g), where g is the induced metric. Then H ≥ nVol(M, g0) where g0 is the hyperbolic metric on M with sectional curvature −1. Equality holds if and only if (M, g) is isometric to (M, g0).
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