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

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3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)3731-3740
Number of pages10
JournalProceedings of the American Mathematical Society
Volume130
Issue number12
DOIs
Publication statusPublished - 2002 Dec 1
Externally publishedYes

Fingerprint

Conformally Flat Manifold
Positive Scalar Curvature
Kleinian Groups
Topology
Geometry
Fundamental Group
Critical Exponents
High-dimensional
Sufficient Conditions

Keywords

  • Conformally flat
  • Convex cocompact
  • Higher A-genus
  • Positive scalar curvature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "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.",
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AB - 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.

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KW - Positive scalar curvature

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