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We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds.
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P.T. Chruściel and G. Nagy, The mass of spacelike hypersurfaces in asymptotically anti – de Sitter spacetimes , Adv. Theor. Math. Phys. 5
2001
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P.T. Chruściel and W. Simon, Towards the classification of static vacuum spacetimes with negative cosmological constant , Jour. Math. Phys. 42
2001
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S. de Haro, S.N. Solodukhin, and K. Skenderis, Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence , Commun. Math. Phys. 217
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X. Wang, Mass for asymptotically hyperbolic manifolds , Jour. Diff. Geom. 57
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M.T. Anderson, P.T. Chruściel, and E. Delay, Non-trivial, static, geodesically complete vacuum spacetimes with a negative cosmological constant , Jour. High Energy Phys. 10
2002
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P.T. Chruściel and E. Delay, Non-singular, vacuum, stationary spacetimes with a negative cosmological constant , Ann. Henri Poincaré 8
2007
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2010
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M. Rupflin, P.M. Topping, and M. Zhu, Asymptotics of the Teichmüller harmonic map flow , Adv. Math. 244
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D.A. Lee and A. Neves, The Penrose inequality for asymptotically locally hyperbolic spaces with nonpositive mass , Commun. Math. Phys. 339
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R. Mazzeo and M. Taylor, Curvature and uniformization , Israel Jour. Math. 130
2002
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T. Sugawa, Estimates of hyperbolic metric with applications to Teichmüller spaces , Kyungpook Math. J. 42
2002
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P.T. Chruściel and M. Herzlich, The mass of asymptotically hyperbolic Riemannian manifolds , Pacific Jour. Math. 212
2003
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C.P. Boyer, K. Galicki, and J. Kollár, Einstein metrics on spheres , Ann. of Math. (2) 162
2005
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M. Herzlich, Mass formulae for asymptotically hyperbolic manifolds , AdS/CFT correspondence: Einstein metrics and their conformal boundaries, IRMA Lect. Math. Theor. Phys., vol. 8, Eur. Math. Soc., Zürich, 2005, pp. 103–121. MR 2160869
2005
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P.T. Chruściel, D. Maerten, and K.P. Tod, Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space- times , Jour. High Energy Phys. 11
2006
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R. Clarkson and Robert B. Mann, Soliton solutions to the Einstein equations in five dimensions , Phys. Rev. Lett. 96
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2015
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E. Woolgar, The rigid Horowitz-Myers conjecture , Jour. High Energy Phys. 3
2016
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2017
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2017
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C. Guillarmou, S. Moroianu, and F. Rochon, Renormalized volume on the Teichmüller space of punctured surfaces , Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 17
2017
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2018
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R. Melrose and X. Zhu, Boundary behaviour of Weil-Petersson and fibre metrics for Riemann moduli spaces , Int. Math. Res. Not. IMRN (2019), 5012–5065. MR 4001023
2019
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R. Bryant, https://mathoverflow.net/questions/396848/einstein-metrics-on-connected-sums/397631#397631 , 2021
2021
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2021
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P.T. Chruściel and E. Delay, On asymptotically locally hyperbolic metrics with negative mass , SIGMA Symmetry Integrability Geom. Methods Appl. 19
2023
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