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We derive a formula of Chern-Gauss-Bonnet type for the Euler characteristic of a four dimensional manifold-with-boundary in terms of the geometry of the Loewner-Nirenberg singular Yamabe metric in a prescribed conformal class.
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1974
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C. R. Graham, Extended obstruction tensors and renormalized volume coefficients
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P. Aviles and R. C. McOwen, Complete conformal metrics with negative scalar curvature in compact Riemannian manifolds
1988
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R. Mazzeo, Regularity for the singular Yamabe problem
1991
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L. Andersson, P. T. Chruściel and H, Friedrich, On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein’s field equations
1992
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C. R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence
1999
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C. R. Graham, Volume and area renormalizations for conformally compact Einstein metrics
2000
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J. A. Viaclovsky, Conformal geometry, contact geometry, and the calculus of variations
2000
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M. Anderson L 2 L^{2} curvature and volume renormalization of AHE metrics on 4-manifolds
2001
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C. Epstein, An asymptotic volume formula for convex cocompact hyperbolic manifolds
2001
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J. A. Viaclovsky, Estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds
2002
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R. Mazzeo and F. Pacard, Poincaré-Einstein metrics and the Schouten tensor
2003
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C. R. Graham and K. Hirachi, The ambient obstruction tensor and Q Q -curvature
2005
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J. Viaclovsky, Conformal geometry and fully nonlinear equations
2006
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S.-Y. A. Chang and H. Fang, A class of variational functionals in conformal geometry
2008
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S.-Y. A. Chang, J. Qing, and P. Yang, On the renormalized volumes for conformally compact Einstein manifolds
2008
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S. Chen, Conformal deformation on manifolds with boundary
2009
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M. J. Gursky, J. Streets and M. Warren, Existence of complete conformal metrics of negative Ricci curvature on manifolds with boundary
2011
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W. Sheng, N. Trudinger, and X.-J. Wang, The k k -Yamabe problem
2012
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W. Sheng, N. Trudinger, and X.-J. Wang, The Yamabe problem for higher order curvatures
2007
Cited alongside, same era.
T. Branson and R. Gover, Variational status of a class of fully nonlinear curvature prescription problems
2008
Cited alongside, same era.
Y. Wang, Boundary expansions of complete conformal metrics with negative Ricci curvatures
Cited in the paper.
2017
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C. R. Graham, Volume renormalization for singular Yamabe metrics
2017
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2018
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