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1 June 2005 Limits of quasi-Fuchsian groups with small bending
Caroline Series
Duke Math. J. 128(2): 285-329 (1 June 2005). DOI: 10.1215/S0012-7094-04-12823-4

Abstract

We study limits of quasi-Fuchsian groups for which the bending measures on the convex hull boundary tend to zero, giving necessary and sufficient conditions for the limit group to exist and be Fuchsian. As an application, we complete the proof of a conjecture made in [24, Conjecture 6.5] that the closures of pleating varieties for quasi-Fuchsian groups meet Fuchsian space exactly in Kerckhoff's lines of minima of length functions. Doubling our examples gives rise to a large class of cone manifolds which degenerate to hyperbolic surfaces as the cone angles approach 2 π .

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Caroline Series. "Limits of quasi-Fuchsian groups with small bending." Duke Math. J. 128 (2) 285 - 329, 1 June 2005. https://doi.org/10.1215/S0012-7094-04-12823-4

Information

Published: 1 June 2005
First available in Project Euclid: 2 June 2005

zbMATH: 1081.30038
MathSciNet: MR2140265
Digital Object Identifier: 10.1215/S0012-7094-04-12823-4

Subjects:
Primary: 30F40
Secondary: 20H10, 32G15

Rights: Copyright © 2005 Duke University Press

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Vol.128 • No. 2 • 1 June 2005
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