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A volume comparison theorem for asymptotically hyperbolic manifolds (1305.6628v1)
Published 28 May 2013 in math.DG
Abstract: We define a notion of renormalized volume of an asymptotically hyperbolic manifold. Moreover, we prove a sharp volume comparison theorem for metrics with scalar curvature at least -6. Finally, we show that the inequality is strict unless the metric is isometric to one of the Anti-deSitter-Schwarzschild metrics.
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