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Convex-cocompactness of Kleinian groups and conformally flat manifolds with positive scalar curvature
Authors:Hiroyasu Izeki
Affiliation:Mathematical Institute, Tohoku University, 980-8578 Sendai, Japan
Abstract:We give a sufficient condition for a higher dimensional Kleinian group $Gamma subset operatorname{Isom} (mathbb{H}^{n+1})$ to be convex cocompact in terms of the critical exponent of $Gamma$. As a consequence, we see that the fundamental group of a compact conformally flat manifold with positive scalar curvature is hyperbolic in the sense of Gromov. We give some other applications to geometry and topology of conformally flat manifolds with positive scalar curvature.

Keywords:Conformally flat   positive scalar curvature   convex cocompact   higher $hat A$-genus
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