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

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We give a sufficient condition for a higher dimensional Kleinian group Γ ⊂ Isom(ℍn+1) to be convex cocompact in terms of the critical exponent of Γ. 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.

元の言語English
ページ(範囲)3731-3740
ページ数10
ジャーナルProceedings of the American Mathematical Society
130
発行部数12
DOI
出版物ステータスPublished - 2002 12 1
外部発表Yes

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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