Proceedings of the American Mathematical Society

Convex-cocompactness of Kleinian groups and conformally flat manifolds with positive scalar curvature

Author(s): Hiroyasu Izeki
Journal: Proc. Amer. Math. Soc. 130 (2002), 3731-3740.
MSC (1991): Primary 58H15; Secondary 53A30
Posted: May 14, 2002
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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.

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