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Limits of quasi-Fuchsian groups with small bending. (English) Zbl 1081.30038
The author studies the limits of quasi-Fuchsian groups for which the bending measures on the convex hull boundary tend to zero, and several necessary and sufficient conditions for the existence and being Fuchsian of the limit group are given. As a consequence, it is proved that the answer to Conjecture \(6.5\) in [Geom. Dedicata 88, 211–237 (2001; Zbl 1005.30032)] raised by the author is positive. A large class of cone manifolds which degenerate to hyperbolic surfaces as the cone angles approach \(2\pi\) has been obtained by doubling the author’s examples.

MSC:
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
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