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In the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature at least -6 and negative mass when the genus of the conformal boundary at infinity is positive.
Black holes in static vacuum space-times
H. Müller zum Hagen, David C. Robinson, and H. J. Seifert · 1973
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Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature
William Meeks, III, Leon Simon, and Shing Tung Yau · 1982
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Uniqueness theorem for anti-de Sitter spacetime
W. Boucher, G. W. Gibbons, and Gary T. Horowitz · 1984
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Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-time
Gary L. Bunting and A. K. M. Masood-ul Alam · 1987
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AdS-CFT correspondence and a new positive energy conjecture for general relativity
Gary T. Horowitz and Robert C. Myers · 1999
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Proof of the Riemannian Penrose inequality using the positive mass theorem
Hubert L. Bray · 2001
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Towards the classification of static vacuum spacetimes with negative cosmological constant
Piotr T. Chruściel and Walter Simon · 2001
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The inverse mean curvature flow and the Riemannian Penrose inequality
Gerhard Huisken and Tom Ilmanen · 2001
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The mass of asymptotically hyperbolic manifolds
Xiaodong Wang · 2001
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The mass of asymptotically hyperbolic Riemannian manifolds
Piotr T. Chruściel and Marc Herzlich · 2003
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On the geometry and mass of static, asymptotically AdS spacetimes, and the uniqueness of the AdS soliton
G. J. Galloway, S. Surya, and E. Woolgar · 2003
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On the rigidity for conformally compact Einstein manifolds
Jie Qing · 2003
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Xiaodong Wang · 2005
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On the Riemannian Penrose inequality in dimensions less than eight
Hubert L. Bray and Dan A. Lee · 2009
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Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
André Neves · 2010
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Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds. II
André Neves and Gang Tian · 2010
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Rigidity of area-minimizing hyperbolic surfaces in three-manifolds, 2011, arXiv:1103.4805
Ivaldo Nunes · 2011
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A volume comparison theorem for asymptotically hyperbolic manifolds, 2013, arXiv:1305.6628
Simon Brendle and Otis Chodosh · 2013
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A positive mass theorem on asymptotically hyperbolic manifolds with corners along a hypersurface
Vincent Bonini and Jie Qing · 2008
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Levi Lopes de Lima and Frederico Girão · 2013
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