A Volumetric Penrose Inequality for Conformally Flat Manifolds
نویسنده
چکیده
We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to Rn \ Ω, n ≥ 3, and so that their boundary is a minimal hypersurface. (Here, Ω ⊂ Rn is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is bounded below by (V/βn) (n−2)/n, where V is the Euclidean volume of Ω and βn is the volume of the Euclidean unit n-ball. This gives a partial proof to a conjecture of Bray and Iga [4]. Surprisingly, we do not require the boundary to be outermost.
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