# 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}
}
• Published 1 November 1999
• Mathematics
• Advances in Theoretical and Mathematical Physics
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 $M… • Mathematics • 2002 Motivated by recent proposals for a de Sitter version of the AdS/CFT correspondence, we give some topological restrictions on spacetimes of de Sitter type, i.e., spacetimes with$\Lambda>0\$, which
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We study in this chapter a class of partial differential equations that generalize and are to a large extent represented by Laplace’s equation. These are the elliptic partial differential equations
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In this chapter we deal with problems concerning Ricci Curvature mainly: Prescribing the Ricci curvature Ricci curvature with a given sign Existence of Einstein metrics.