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We define a mass-type invariant for asymptotically hyperbolic manifolds with a noncompact boundary which are modelled at infinity on the hyperbolic half-space and prove a sharp positive mass inequality in the spin case under suitable dominant energy conditions.
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S. Brendle, F. C. Marques, Recent progress on the Yamabe problem. Surveys in geometric analysis and relativity
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L. L. de Lima, F. Girão, A. Montalbán, The mass in terms of Einstein and Newton, arXiv:1811.06924
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S. Almaraz, E. Barbosa, and L. L. de Lima, A positive mass theorem for asymptotically flat manifolds with a non-compact boundary. Commun. Anal. Geom
2016
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L.L. de Lima, F. Girão, An Alexandrov–Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality, Ann. Henri Poincaré 17 (2016) 979–1002
2016
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M. Herzlich, Computing asymptotic invariants with the Ricci tensor on asymptotically flat and asymptotically hyperbolic manifolds. Ann. Henri Poincaré
2016
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G. Li, J. Qing, Y. Shi, Gap phenomena and curvature estimates for conformally compact Einstein manifolds, Trans. Amer. Math. Soc
2017
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