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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Hiroyasu Izeki
Journal: Proc. Amer. Math. Soc. 130 (2002), 3731-3740
MSC (1991): Primary 58H15; Secondary 53A30
Published electronically: May 14, 2002
MathSciNet review: 1920055
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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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Additional Information

Hiroyasu Izeki
Affiliation: Mathematical Institute, Tohoku University, 980-8578 Sendai, Japan
Email: izeki@math.tohoku.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06504-8
PII: S 0002-9939(02)06504-8
Keywords: Conformally flat, positive scalar curvature, convex cocompact, higher $\hat A$-genus
Received by editor(s): March 19, 2001
Received by editor(s) in revised form: July 31, 2001
Published electronically: May 14, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society