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Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

2015; Springer Science+Business Media; Volume: 47; Issue: 3 Linguagem: Inglês

10.1007/s10714-015-1870-z

1572-9532

Levi Lopes de Lima, Frederico Girão,

Geometry and complex manifolds

We establish versions of the positive mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions $$n\ge 3$$ an optimal Penrose inequality for certain graphs in hyperbolic space $$\mathbb {H}^{n+1}$$ whose boundary has constant mean curvature $$n-1$$ . This settles, for this class of manifolds, an inequality first conjectured by Wang (J Differ Geom 57(2):273–299, 2001).