Given a geometrically finite hyperbolic cone-manifold, with the cone-singularity sufficiently short, we construct a one-parameter family of cone-manifolds decreasing the cone-angle to zero. We also control the geometry of this one-parameter family via the Schwarzian derivative of the projective boundary and the length of closed geodesics

Bromberg, K.

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Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives

Approximation by maximal cusps in the boundaries of quasiconformal deformation spaces.

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Boundaries of deformation spaces and Ahlfors’ measure conjecture.

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https://authors.library.caltech.edu/25351/1/BROjams04.pdf

Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives

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