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Limits of quasi-Fuchsian groups with small bending
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UNSPECIFIED (2005) Limits of quasi-Fuchsian groups with small bending. DUKE MATHEMATICAL JOURNAL, 128 (2). pp. 285-329. ISSN 0012-7094.
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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-Fitchsian groups meet Fuchsian space exactly in Kerckhoffs 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 pi.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | DUKE MATHEMATICAL JOURNAL | ||||
Publisher: | DUKE UNIV PRESS | ||||
ISSN: | 0012-7094 | ||||
Official Date: | 1 June 2005 | ||||
Dates: |
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Volume: | 128 | ||||
Number: | 2 | ||||
Number of Pages: | 45 | ||||
Page Range: | pp. 285-329 | ||||
Publication Status: | Published |
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