Hyperbolic cone-manifolds, short geodesics and Schwarzian derivatives

Kenneth Bromberg

Hyperbolic cone-manifolds, short geodesics and Schwarzian derivatives

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arxiv math/0211401 v1 pith:GB5SPGDL submitted 2002-11-26 math.GT math.DG

Kenneth Bromberg This is my paper · ORCID

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keywords conecone-manifoldsfamilygeodesicshyperbolicparameterschwarzianshort

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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.

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Expansion joints in hyperbolic manifolds
math.GT 2025-11 conditional novelty 7.0 of 10

Cone-deforming an ideal arc through 'expansion joints' interpolates between stacked Borromean ring complements and lantern manifolds, and yields cone deformations of highly twisted 2-bridge unknotting tunnels.

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