Journal of Mathematics of Kyoto University

On strong convergence of hyperbolic 3-cone-manifolds whose singular sets have uniformly thick tubular neighborhoods

Michihiko Fujii

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Abstract

Let $C$ be a compact orientable hyperbolic 3-cone-manifold with cone-type singularity along simple closed geodesics $\Sigma$. Let $\{ C_{i}\}_{i=1}^{\infty}$ be a sequence consisting of deformations of $C$ and $\Sigma _{i}$ be the singular set of $C_{i}$ so that the cone angles along $\Sigma _{i}$ all are less than $2\pi$. In this paper, we will show that, if tubular neighborhoods of the singular sets $\Sigma _{i}$ can be taken to be uniformly thick, then there is a subsequence $\{ C_{i_{k}}\}_{k=1}^{\infty}$ which converges strongly to a hyperbolic 3-cone-manifold $C_{*}$ homeomorphic to $C$.

Article information

Source
J. Math. Kyoto Univ., Volume 41, Number 2 (2001), 421-428.

Dates
First available in Project Euclid: 17 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250517641

Digital Object Identifier
doi:10.1215/kjm/1250517641

Mathematical Reviews number (MathSciNet)
MR1852992

Zentralblatt MATH identifier
1002.57040

Subjects
Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 30F40: Kleinian groups [See also 20H10] 57M50: Geometric structures on low-dimensional manifolds 57N10: Topology of general 3-manifolds [See also 57Mxx]

Citation

Fujii, Michihiko. On strong convergence of hyperbolic 3-cone-manifolds whose singular sets have uniformly thick tubular neighborhoods. J. Math. Kyoto Univ. 41 (2001), no. 2, 421--428. doi:10.1215/kjm/1250517641. https://projecteuclid.org/euclid.kjm/1250517641


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