Boundaries of zero scalar curvature in the AdS / CFT correspondence

@article{Cai1999BoundariesOZ,
  title={Boundaries of zero scalar curvature in the AdS / CFT correspondence},
  author={Mingliang Cai and Gregory J. Galloway},
  journal={Advances in Theoretical and Mathematical Physics},
  year={1999},
  volume={3},
  pages={1769-1783}
}
In hep-th/9910245, Witten and Yau consider the AdS/CFT correspondence in the context of a Riemannian Einstein manifold $M^{n+1}$ of negative Ricci curvature which admits a conformal compactification with conformal boundary $N^n$. They prove that if the conformal class of the boundary contains a metric of positive scalar curvature, then $M$ and $N$ have several desirable properties: (1) $N$ is connected, (2) the $n$th homology of the compactified $M$ vanishes, and (3) the fundamental group of $M… 

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