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

Hiroyasu Izeki

doi:10.1090/S0002-9939-02-06504-8

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

Hiroyasu Izeki

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	3731-3740
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	130
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9939-02-06504-8
Publication status	Published - 2002 Dec 1
Externally published	Yes

Keywords

Conformally flat
Convex cocompact
Higher A-genus
Positive scalar curvature

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-02-06504-8

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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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AU - Izeki, Hiroyasu

PY - 2002/12/1

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N2 - 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.

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.

KW - Conformally flat

KW - Convex cocompact

KW - Higher A-genus

KW - Positive scalar curvature

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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